The Italian took charge of the Spanish club last summer after leaving Paris Saint-Germain.
Los Blancos have had a successful season so far under Ancelotti. The Madrid outfit have already won the Copa del Rey and remain in contention for La Liga and UEFA Champions League glory.
However, Ancelotti has been linked with the vacant managerial job at Old Trafford since the dismissal of David Moyes on Tuesday.
The Red Devils have put Ryan Giggs in charge of the first team until the end of the season, but the Welshman is currently not one of the favourites to take over on a full-time basis.
Ancelotti is one of a number of candidates who are said to be on United's list, but the former AC Milan coach has insisted that he has no plans to leave Madrid any time soon.
"I'm happy here at Real Madrid," the 54-year-old, who won the Premier League and the FA Cup with Chelsea in 2009-10, told reporters.
"I am lucky to be working at the best club in the world and my place is here.
"I respect Man United a lot. I was disappointed for David Moyes, but my place at the moment is here."