"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 meanwhile took to Twitter to deny the story.
"The Independent are talking absolute rubbish. My future is with Manchester United and the club and I are totally committed to each other ,The manager and I have no issues and anyone who says different don't know what they are talking about," the striker added.
Fresh speculation about strains in Ferguson and Rooney's relationship began during the Christmas holiday programme, when it emerged the player had been dropped from last week's defeat against Blackburn.
Rooney was fined a week's wages after going out for dinner with his wife and fellow players Jonny Evans and Darron Gibson on December 26.
A lacklustre Rooney was also substituted by Ferguson during Wednesday's 3-0 defeat against Newcastle at St James Park.