The former Reds striker told MUTV that the current Everton boss should not be compared to his fellow Scot Sir Alex Ferguson but must be given every chance to continue the story of success at Old Trafford.
"To be honest, I think I find it hard to think of another candidate that fits the bill so well," Dublin said. "I think he's got the attributes, the ethic and he knows the club incredibly well, which I think is important.
"I think he will do well. I can't see anyone more qualified than him.
"But Sir Alex will not be matched - there is nobody like him. You have to say: 'Mr Moyes, take the club forward in your own way but take it forward and make us win trophies. Let the fans see the kind of football they want to see but keep us at the same standard as Sir Alex as you can't compare them in any way, shape or form'."