Coleman is certain the Scot can handle the switch to one of the biggest jobs in world football.
He told the Daily Mail: "I think Alex Ferguson had a big say in who the manager would be so he must see something good in him. He has that longevity too. He's been at Everton for 10 years and that's maybe something Alex Ferguson looked at.
"He's done so well with Everton over the last 10 years, top eight every year with maybe not the budget everyone else has. He always manages to pick up good players.
"There is expectancy. We'll have to wait and see but I'm sure he wouldn't take on a job like that if he didn't believe in his own ability. I can only speak about my time at Everton with him and he's been brilliant with me and I wish him the very best and hope he can have continued success at Manchester United. I owe him an awful lot."