Louis van Gaal was sacked by the club on Monday after a disappointing two years at the helm that saw him win just one trophy - the FA Cup last weekend.
But Ancelotti, who will take charge of Bayern Munich this summer, believes Van Gaal had a tough job from the very start - but appreciates Mourinho will make a good successor.
“I think it is a good wedding [with United] because Mourinho really knows the Premier League well," Ancelotti told The Telegraph.
"He is one of the best coaches in the world and Manchester United at this moment need someone who can improve what they did in the last two years with Louis van Gaal.
“There are different opinions about the job of Van Gaal, no?
"My opinion is that he arrived in a moment when he needed to rebuild a team after Rio Ferdinand, after [Paul] Scholes, after [Ryan] Giggs, after Ferguson and it takes time. The same thing happened to Milan.
"When Milan lost [Paolo] Maldini, [Gennaro] Gattuso, [Filippo] Inzaghi it was difficult to rebuild the team quickly, they needed time.
"The last year they [United] showed they have really good young players. And maybe with Mourinho they could have a step forward.”
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