Reports this week have claimed Rooney's agent, Paul Stretford, travelled to China to negotiate with Chinese clubs potentially ready to offer the England captain a lucrative exit from the Premier League.
The Chinese transfer window remains open until the end of February, meaning a deal could have been struck with immediate effect.
In a statement released to the Press Association, Rooney said: "Despite the interest which has been shown from other clubs, for which I’m grateful, I want to end recent speculation and say that I am staying at Manchester United.
"I hope I'll play a full part in helping the team in its fight for success on four fronts. It’s an exciting time at the club and I want to remain a part of it."
On Wednesday, Tianjin Quanjian coach Fabio Cannavaro admitted his club had approached Rooney but ruled out a move on the grounds that he did not fit his preferred style of play.
Beijing Guoan have been linked with the 31-year-old on the basis that they remain under the quota of foreign players allowed in the Chinese league, though Jiangsu Suning had also been tipped as a possible destination despite currently being at the limit.
Rooney has scored two goals in 17 league matches this season, eight of which have been starts.
He began the campaign as a member of Jose Mourinho's starting XI but has since fallen out of the lineup, with Zlatan Ibrahimovic now the club's first-choice striker and Paul Pogba and Henrikh Mkhitaryan bolstering the midfield.