However, the Welshman is not expected to get the vacancy on a permanent basis as the Red Devils board seek a man of experience, with outgoing Netherlands coach Louis van Gaal the current frontrunner.
Wilkins, who worked with Ancelotti during the Italian's Chelsea tenure, has advised the club that he spent five years with to swoop for the Madrid manager if they decide to axe him in the summer.
"I think Manchester United will go for an experienced manager. David Moyes was the right man last year after his time at Everton, but the name that jumps out at me is Carlo Ancelotti," he told Sky Sports News.
"The Copa del Rey is not enough for Real Madrid, so if he doesn't win La Liga or the Champions League, he may become available. He speaks English, knows the Premier League and I think he would be ideal."
Ancelotti won the Premier League and FA Cup double in his first season in charge at Stamford Bridge, but was sacked a year later and has since managed Paris Saint-Germain to the Ligue 1 title.