The Dutchman is yet to win a competitive fixture with the Red Devils, who appointed Van Gaal following last season's disastrous campaign under David Moyes.
The North-West outfit fell from champions to seventh in the Premier League after Sir Alex Ferguson retired following 27 years at the helm of Old Trafford.
Mourinho told Eurosport-Yahoo: "He is one of the best managers in the world, so I think he is a man with great experience for the job. Manchester United is a big team, he is a big manager, so I think they will do well together."
Mourinho worked alongside Van Gaal for three years during the pair's time together at Barcelona.