This year the side played five fixtures in the United States, where they faced the likes of Barcelona, Real Madrid and arch rivals Manchester City as part of the annual International Champions Cup competition.
For next summer United are reportedly keen to visit the Far East, where they have a huge fanbase, but Mourinho is said to prefer another trip to the US.
"The club have looked at playing in the Far East next summer as part of a tournament," a source told The Sun. "Jose won't be happy about this and will be speaking to the money men upstairs who arrange it all.
"United have a huge amount of supporters out there and plenty of commercial capability, but Jose wants to go to the US."
Last summer Mourinho took his United squad to China and was less than complimentary about the standard of the facilities, while their planned friendly against City at the Bird's Nest in Beijing was called off at the last moment following torrential rain.