Cottee believes Moyes will be on Manchester United’s list of targets for when Fergie decides to retire.
Cottee said: “There are only about half-a-dozen managers in world football who could fill the boots of Sir Alex Ferguson.
“I believe David Moyes is one of those. Martin O’Neill could do it, Jose Mourinho could do it and two or three others could.
“How do follow the best manager in football ever?
“It will be a very difficult job for anyone but I think David Moyes is capable of rising to that challenge and handling the pressures that come at Old Trafford.
“I don’t want to see Moyes leave Everton because he is doing a great job there and I want to see him finish the job he has started.
“He is building a dynasty, trying to get back to the glories of the Eighties.
“But they really need to win a trophy or get into the Champions League so you can attract the best players.”
Cottee added: “Most clubs’ best players are always vulnerable to other clubs, Mikel Arteta is linked with a move to a number of clubs because Everton haven’t won anything.
“If Moyes can change that and lift a trophy then the better players, like Arteta, Pienaar and Cahill, won¹t want to move anywhere else because Everton are a fantastic football club to play for.”