Reports that Mohammed Bin Salman intends to buy the club are "completely false", the minister, Turki al-Shabanah, wrote on social network Twitter.
He was reacting to reports that the crown prince had sought to tempt the Glazer family to cede control of the club.
"Manchester United held a meeting with PIF Saudi to discuss (a) sponsorship opportunity," Shabanah said, adding that no deal materialised.
On Sunday, the British newspaper, the Sun, said the crown prince was in a £3.8-billion ($4.9-billion) takeover bid for one of football's most popular clubs.
The paper said a bid was first submitted in October but the fallout from the murder of Saudi journalist Jamal Khashoggi at the kingdom's embassy in Istanbul put the "skids" on a potential offer.
(Reporting by Hadeel Al Sayegh; Editing by Clarence Fernandez)
