The former Stamford Bridge assistant believes that Sir Alex Ferguson's ability to bring the best out of experienced players at Old Trafford makes it the perfect destination for the 34-year-old, whose contract with the Blues expires in June.
"He'll want to continue to win and play at a high level - and there's no higher level than Old Trafford," Wilkins told BBC Sport. "You have the master of utilizing the older player in Sir Alex Ferguson, so I think it would be a tremendous move for Frank and a good one for Manchester United as well.
"You only have to see the performances [Ryan] Giggs and [Paul] Scholes have put in over the last few years - and they are four years older than Frank."
The former United captain dismissed claims that the midfielder would be poorly received at Old Trafford due to his Chelsea links, insisting the fans would appreciate his ability.
"He'll win them over because of his footballing ability," he said.