Cole says Fernandes is now too good for United.
"I think it could be a natural separation for Fernandes and Manchester United," Cole said, according to the Daily Mail.
"He's not a perfect footballer, like Steven Gerrard, Paul Scholes or Kevin De Bruyne, but he's a brilliant player who has been fantastic for Manchester United during the club's toughest period in about 40 years."
Cole also stated: "He can hold his head high for what he has achieved at Manchester United, but I think he deserves to play in a better team. It would be a good separation for the club, and it would benefit both of them. Manchester United need players who do things that don't suit Bruno."
Fernandes' contract with United runs until the summer of 2027, with an option for a further year.