Health Secretary Jeremy Hunt will reportedly replace Damian Green as May's de facto deputy during the Monday government reshuffle.
Green resigned from his role as first secretary of state after a cabinet investigation discovered that the politician had misled the public and fellow politicians over pornography found on his office computer.
The reshuffle may also see the sacking or the demotion of Education Secretary Justine Greening, as well as Tory chairman Patrick McLoughlin, Commons Leader Andrea Leadsom and Business Secretary Greg Clark.
At the same time, British media cited government sources as saying that the so-called "big four", including Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd and Brexit Secretary David Davis, will remain in their posts.
Monday's major minister shake-up will allow for more women and younger MPs to be given roles at junior ministerial levels on Tuesday.
Likely candidates for promotion will reportedly include government aide Suella Fernandes, head of the party’s European Research Group, and Seema Kennedy, May's parliamentary private secretary.
Meanwhile, the British Prime Minister's former policy adviser George Freeman has urged Theresa May "to be bold" and conduct her cabinet reshuffle in order to strengthen the government and indicate that Brexit could be "a moment of renewal," according to the Financial Times.