Stories have emerged claiming the 26-year-old's relationship with Sir Alex Ferguson is broken beyond repair.
This has been denied by both parties.
"Manchester United and Wayne Rooney have been made aware of the theme of an article in tomorrow's [Sunday] Independent newspaper," said the statement.
"We have not seen the detail but can assure all United fans that 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.
"Any suggestion that Manchester United and Wayne Rooney are to part company is complete nonsense."
Rooney himself said on Twitter: "The independent are talking absolute rubbish, my future is with Manchester United and the club and I am totally committed, the manager and I have no issues and anyone who says different doesn't know what they are talking about."
Rooney was disciplined by Ferguson last week after he became aware of the player having a night out on Boxing Day, immediately after the 5-0 win over Wigan.
It is not believed to be the night out itself that angered Ferguson but Rooney's subsequent performances in training.
Rooney was fined, believed to be a week's wages, and it is also claimed he was dropped for the home defeat by Blackburn on New Year's Eve as punishment.
This has not been confirmed by Sir Alex Ferguson, who refused to discuss the matter at his press conference to preview the FA Cup third-round tie with Manchester City.
Indeed, Ferguson offered only the briefest of responses to questions about the reason for Rooney's below-par performance at Newcastle on Wednesday.
"It is not a crime to try too hard," said Ferguson, when asked whether his star player's desperation to succeed was the issue.
The speed with which Saturday's rebuttal has been released does indicate any problems between Ferguson and Rooney have been ironed out.
This will come as a relief to United fans, who have seen their side slip three points adrift of City in the Premier League title race and head to the Etihad Stadium on Sunday in the unusual position of underdogs for a Manchester derby.