Mourinho, 55, walks away from Old Trafford with a £24m pay-off after failing to repeat the success he had enjoyed at Chelsea and Real Madrid.
"A caretaker-manager will be appointed until the end of the season while the club conducts a thorough recruitment process for a new, full-time manager," United said in a statement.
Mourinho is the third manager at United since Sir Alex Ferguson retired — following the equally unsuccessful David Moyes and Louis Van Gaal.
Man Utd appointing a caretaker manager until the end of the season is a clear indication that they’ve as good as thrown the towel in on this season. #mufc #Mourinho
— Martin Tooth (@Toothy73) 18 December 2018
So who is the long-term answer to United's management problem?
Zinedine Zidane
The Frenchman is the early betting favourite with odds as short at 6-4 with Sportingbet.
A midfield genius who led France to the World Cup in 1998 and the European Championships in 2000 but blotted his copybook slightly when he was sent off in the 2006 World Cup final for headbutting Italian defender Marco Materazzi.
Zizou, as he was nicknamed, spent most of his career at Juventus and Real Madrid and has never played or managed in the English Premier League, which may be seen as a negative.
Glazers at Manchester United: impose £525m debt, appoint their banker Ed Woodward to run club; fail to plan Ferguson succession, burn through managers' reputations including Mourinho; take ££ms in dividends.
— David Conn (@david_conn) 18 December 2018
But Pep Guardiola had also never played or managed in England but has been a big hit across Manchester with City.
Zidane was appointed manager of Real Madrid in 2016 and won La Liga, the Champions' League and the World Club Cup in his first season.
He won another Champions' League trophy earlier this year — beating Liverpool — but resigned a few days later.
United have made it clear they do not plan a long-term appointment until the summer so they may lose out on Zidane if another big job comes up in the next six months.
Eddie Howe
The leading English contender for the job is undoubtedly Bournemouth manager Eddie Howe who led the club from the fourth tier of English football to the Premier League, where they are holding their own and regularly beating the top sides.
He has done it by playing an attractive style of football and bringing through talented youngsters — both of which are traits which Mourinho lacked.
Man Utd have done the easy bit and sacked Mourinho, whose negativity has infected the whole playing side. The harder part is changing the club, which is a commercial deal-making factory gone wrong.
— Paul Hayward (@_PaulHayward) 18 December 2018
Going for Howe would be a bold choice as he is only 41 and lacks any experience in the Champions' League.
He has also only been successful at one club — the team where he spent most of his playing career — and had a less than happy spell at Burnley. He resigned from there for "personal reasons" in October 2012.
If Howe did go to United, expect him to go back to Bournemouth and snap up several of their exciting players — including striker Callum Wilson and defender Nathan Ake.
Michael Carrick
The former Manchester United and England midfielder is assistant coach at the club and is seen as managerial material in the future but he has been overlooked for the job of caretaker-manager and that could suggest the Glazers, who own the club, do not trust him with the team long-term.
Carrick, 37, joined United from Tottenham in 2006 and played 464 games for the Red Devils in an illustrious career, mainly under Sir Alex.
Interim manager at @ManUtd will be Ole Gunnar Solksjaer. You heard it here first #mufc
— Mario Cacciottolo (@m_cacciottolo) 18 December 2018
Carrick opened up earlier this year on his battle with depression, which he said hit him for two years after the 2009 Champions' League final against Barcelona, which United lost. Carrick said he blamed himself for giving the ball away and said it led to the "biggest low" in his career.
Mauricio Pochettino
Although he has not yet won a single trophy in England, Tottenham manager Mauricio Pochettino's reputation is through the roof at the moment.
Spurs finally ended above their north London arch-rivals Arsenal last season and qualified for the Champions' League, where they have been drawn against Borussia Dortmund in the last 16.
Pochettino has also played attractive, flowing football at Tottenham and his previous club, Southampton, and United's fans are crying out for entertainment after almost three years of dour and defensive soccer under Mourinho.
But if Spurs win a trophy — the FA Cup perhaps — and qualify for the Champions' League and United do neither, will Pochettino really want to walk away from the London club with their magnificent new stadium to try and resurrect a United club which is lacking in superstars of the calibre of Harry Kane and Dele Alli?
And how much would it cost United to prise him away from Tottenham's chairman David Levy, a man who forced Real Madrid to pay top dollar for Gareth Bale and is not known for giving away his best assets?
Antonio Conte
Paddypower are offering odds of 2-1 for the former Chelsea and Italy manager taking over at Old Trafford.
Conte won the Premier League in his first season with Chelsea but his second was a disappointment with the club finishing only fifth in the table and even winning the FA Cup — against United — was not enough to save the Italian from the sack.
Conte is out of a job after being sacked by Chelsea in the summer and would be the ideal man for the caretaker role at Old Trafford.
If he was able to somehow steer United's moribund squad into the top four in the Premier League — meaning qualification for the Champions' League — he might just persuade the Glazers and chief executive Ed Woodward to give him the job full-time.
Laurent Blanc
The former French international defender Laurent Blanc is one of the few contenders who have actually played for United.
Blanc played 48 games for United in the twilight of his career and his still remembered affectionately at Old Trafford for his role at the centre of Sir Alex's defence.
He went on to manage both France and Paris St Germain, where he was nicknamed Le President by players for his managerial style.
After three successful years at PSG he left in July 2016 and has been out of work since.
Blanc again may be one of the names the club has in mind to be a caretaker manager but whether he is the man for the long-term task of rebuilding the United team remains to be seen.
Leonardo Jardim
Do United want a Portuguese manager to replace the Setubal-born Mourinho?
Perhaps not, but if they do they might opt for Leonardo Jardim, who had a very successful spell as coach of Monaco.
He left the club in October this year and would jump at the chance of managing United.
But whether his name and reputation is big enough to satisfy United fans is doubtful.
Nuno Espirito Santo
Another Portuguese manager whose reputation is growing day by day is Nuno Espirito Santo, who led Wolverhampton Wanderers to promotion in his first season.
Wolves have surged to seventh place in the Premier League and are just one point behind United despite working on a fraction of their budget.
They have won their last three games, including a magnificent 2-1 victory over Chelsea on December 5.
Nuno has also achieved this success by playing an attractive and buccaneering style which would transfer well to the "Theatre of Dreams".
But he would be a massive outsider to get the job as he has only been a top flight manager for a very short time and his CV also includes a fairly unsuccessful spell with Porto.
Ryan Giggs
Giggs is an absolute legend at Old Trafford and he was talked off as a possible manager after Moyes left and again when Van Gaal was ousted.
But after a spell coaching at United, Cardiff-born Giggs chose to go into management with the Welsh national team earlier this year.
Giggs is still cutting his teeth as a manager and his reputation took a bit of a battering last month when Wales lost to Albania in a friendly.
Brendan Rodgers
Rodgers is riding high as manager of Glasgow Celtic, who have dominated Scottish football for the last decade.
But whether that means he is qualified to take over at United is another thing.
The Ulsterman also has another negative in his column — he was once manager of arch-rivals Liverpool.
Very few players or managers have gone from Anfield to Old Trafford or vice versa and it might be difficult to sell Rodgers to the United faithful.
Arsene Wenger
A complete outsider would be former Arsenal manager Arsene Wenger, who had several run-ins with Sir Alex Ferguson during their times in charge of their respective clubs.
But the relationship between the pair warmed towards the end and Fergie paid a glowing tribute to Wenger when he left Arsenal at the end of last season.
Wenger, at 69, is by far the oldest of the contenders and would be greeted with dismay by most United fans.
But he would be a good choice as caretaker manager for the rest of the season and his man management skills could be deployed to good effect on Paul Pogba, the club's star midfielder who has been engaged in a personal war with Mourinho this season.
