According to the newspaper, which quotes four current and former American officials and Saudis close to the royal family, the restrictions have been placed on bin Nayef to limit any potential opposition from him to the newly proclaimed crown prince, 31-year-old Mohammed bin Salman, the son of King Salman, whom the king appointed unexpectedly, breaking a decades-long rule of succession.
Prince Mohammed bin Salman is known both for his work dealing with the al-Qaeda insurgency between 2003 and 2006, and for more recent economic and social reforms.
The allegations of bin Nayef's house arrest were refuted by Saudi officials on Thursday.
According to a Reuters report, a senior Saudi official "expressed shock at the [New York Times] report, which he described as a ‘fabricated story' and suggested that Mohammed bin Nayef may seek legal action against the newspaper."
"His Royal Highness Prince Mohammed bin Nayef and his family is moving freely and hosting his guests unrestrictedly. Nothing has changed for Prince Mohammed, except for stepping down from his government positions," the official said.
The US State Department acknowledged that they are "aware" of reports of bin Nayef's alleged confinement, but said they are unable either confirm or deny the allegations.
Prince bin Salman has been referred to as "Mr. Everything" by diplomats, because of the vast scope of power he already has within the kingdom, according to a Newsweek report. Apart from pushing Saudi Arabia on the Vision 2030 reform program, he has also been tasked with meeting world leaders, such as Russian President Vladimir Putin and US President Donald Trump, in place of his aging father.