Mourinho controversially claimed earlier this week that United were paying over the odds for Luke Shaw, a B£27million signing from Southampton who reportedly now earns in the region of B£100,000 a week.
Mourinho said had Chelsea paid that kind of money to the 19-year-old, it would have "killed" the London club.
United boss Van Gaal hinted he would speak privately to Mourinho about the matter. Many saw that as a sign the two former colleagues were set for a rocky relationship this season.
Mourinho, who worked as Van Gaal's assistant at Barcelona for three years, has a record of trying to wind up fellow managers.
But Van Gaal is sure he will have a harmonious relationship with the Portuguese this term even though both he and his former protege are in charge of teams vying for the title.
"I don't think I will fall out with him. He is my friend," Van Gaal said of Mourinho.
"I don't think (I will fall out with) all the other managers. I have full respect for all my colleagues.
"For me (mind games) are not so interesting. I have to manage my club.
"That is already difficult enough. I am not concerned with other clubs or other managers."
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- Van Gaal