The pair meet in the Community Shield at Wembley this weekend.
Coyle said: "I never had any doubts he would do well [in management] because he's such a well-grounded and humble man.
"He was the right successor to Sir Alex and straight away he's come in and had trials and tribulations to deal with, with the stuff going on, but he's dealt with it well as he always does.
"There's huge transfer speculation at United but he'll bring his players in at the right time and the one thing about him is, when he's chasing quality players, he's very studious about it and makes sure he gets the right type. He'll do that at Manchester United."
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