Ancelotti has a close personal relationship with Sir Alex Ferguson, someone new United CEO Richard Arnold has sought advice from since taking over from Ed Woodward earlier this year.
United are hopeful of making a long-term appointment ahead of next season after drawing up a five-man shortlist which includes Mauricio Pochettino and Erik ten Hag.
Sources have told ESPN that Ferguson is an admirer of Pochettino but has recommended that the club consider Ancelotti if the former Tottenham Hotspur boss rules himself out of the running.
Ancelotti, in charge at Real Madrid, is seen as the type of coach who could be successful during a short stint because of his extensive experience in the Premier League and Champions League while also having a track record of managing squads full of high-profile players.
Ralf Rangnick, who was placed in charge temporarily following Ole Gunnar Solskjaer's dismissal in November, has also said he could recommend to the board that he stays in the role for another year.
"We are now conducting a thorough process for the appointment of a new permanent manager who will take charge this summer, with the objective to get us back to challenging for those domestic and European titles," football director John Murtough said at a fans' forum held last week.
United would prefer to have a long-term manager in place before the start of next season but there are complications with a number of their top targets.
Pochettino has been linked with a move to Real Madrid to replace Ancelotti while there have been suggestions Ten Hag has reservations about the set-up at Old Trafford having worked well within a clearly defined structure at Ajax.
Ancelotti has guided Real Madrid to a six-point lead at the top of LaLiga but the 62-year-old has faced criticism following his team's performance against Pochettino's Paris Saint-Germain in their Champions League round-of-16 first leg.
It has led to speculation Real Madrid could target Pochettino in the summer with the Argentinian said to be ready to leave PSG.
He has also won the Champions League three times, including with Cristiano Ronaldo at Real Madrid in 2014.