The Dane has been unable to usurp David de Gea as the first-choice shot-stopper this season although Lindegaard did enjoy a five-game stint in the side in November when the Spaniard was injured.
Earlier in the campaign there was speculation that Lindegaard could seek an exit in order to secure first-team football elsewhere and, with the transfer window approaching, the United keeper could again find himself linked with an exit.
However, the 29-year-old has stressed he has no desire to leave the newly-crowned Premier League champions.
"When players get to Manchester United they don't won't to leave. You're part of a family, and now I feel the same. I have no intentions of leaving," Lindegaard is quoted as saying by ESPN.
United boss Sir Alex Ferguson signed Lindegaard in the January transfer window in 2011 but his arrival was overshadowed by the £19million capture of De Gea the following summer.
After battling the Spaniard for the number one spot for a short period, he found himself as the club's number two.
Ferguson, who will manage United for the last time at West Brom on Sunday, has already confirmed that Lindegaard will start in the final fixture of the campaign and the keeper is keen to battle for a regular first-team role under incoming manager David Moyes.
"I'm not going to wave the white flag and give up here," he added. "I'm fighting for the position even though David de Gea is my good friend but I still want the number one shirt. Nothing has changed from one year ago or six months ago."