The main story on the back page of Saturday's Independent said the "Christmas bust-up between Rooney and Ferguson has run so deep that it could lead to the player's departure as early as the current transfer window."
United and Rooney responded swiftly by issuing a joint denial late on Friday night.
"Any suggestion that Manchester United and Wayne Rooney are to part company is complete nonsense," the club and the player said in a statement on United's website.
"We have not seen the detail [of the report] but can assure all United fans the manager and the club are committed to Wayne Rooney and Wayne is committed to the manager and the club.
"The player and the manager have always had and retain the utmost respect for each other and look forward to working together in the coming seasons."
According to several media reports earlier this week, Rooney was dropped for last Saturday's 3-2 Premier League home defeat by Blackburn Rovers for "disciplinary reasons."
United rarely comment on internal disciplinary matters but the reports said Rooney was fined a week's wages for going on a night out with team-mates Darron Gibson and Jonny Evans.
The England striker returned to the team for the 3-0 league defeat at Newcastle United on Wednesday but was substituted in the second half after a below-par performance.
Manchester United's next fixture is an FA Cup Third Round clash at holders Manchester City on Sunday.
