David Moyes was sacked by the fallen Premier League champions on Tuesday, just 10 months after replacing long-serving manager Sir Alex Ferguson.
Outgoing Netherlands coach Louis van Gaal is the early favourite to take charge at Old Trafford once the FIFA World Cup concludes in July.
Former Chelsea assistant Wilkins, who was Ancelotti's right-hand man during his spell in London, said he believes the Italian would be the ideal man for the job.
"I think Manchester United will go for an experienced manager," Wilkins told Sky Sports News.
"David Moyes was the right man last year after his time at Everton, but the name that jumps out at me is Carlo Ancelotti."
Despite winning the Copa del Rey, a failure to claim further silverware could spell the end of Ancelotti's tenure at the Bernabeu, according to Wilkins.
"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 said.
"He speaks English, knows the Premier League and I think he would be ideal."
