The Real Madrid coach, having just won the Champions League for the third time, has backed the former striker as the right man to replace Clarence Seedorf at San Siro
Seedorf looks set to depart the Italian giants following a dispute with the club's management, and Silvio Berlusconi and Adriano Galliani have pinpointed Inzaghi as his replacement.
And Ancelotti believes the former Italy international - whom he coached during his time at San Siro - could be a huge success should he take charge of the senior team.
"Pippo has an extraordinary enthusiasm, a great desire, and has prior experience in the youth area," Ancelotti told reporters. "He certainly has all the features to [do well at Milan]... If he becomes coach, I wish him good luck."
Meanwhile, the three-time Champions League winning coach also admitted an interest in taking the Italy job in future.
"Coaching the your country's national side is always a goal," said the 54-year-old. "But [for the time being] I still want to be on the [training] field every day, I very much enjoy the daily relationship with the team.
"When I am no longer having fun ... I'll call the Italian Football Federation [FIGC]. When Prandelli's contract expires [in 2016]," he jokingly added.