Fletcher has only made 15 appearances, nine as substitute, for the club so far this season.
“I am still happy playing for Manchester United and I am not thinking of going elsewhere,” he said.
“I never heard anything about Birmingham being interested, I just know I want to be here for a long time.
“My only focus is on being ready when the manager needs me and being able to perform for the club when asked.”
He added: “It is frustrating because any player wants to play.
“But basically, it has been down to the form of the midfield. Fair play to Anderson, when Paul Scholes got injured, he came in and has been in great form.
“The manager has stuck by him, which is what he does when you perform well, and has had a run in the team.
“We will see how things pan out at the end of the season in terms of games played and what you have contributed to the squad. But I am not thinking about that just now.
“I am just looking to the short term, and I would like to win a few trophies and hopefully go a few steps further than last year.”
