Mourinho controversially claimed earlier this week that United were paying over the odds for Luke Shaw, a £27million signing from Southampton who reportedly now earns in the region of £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.”
Although he has only been in position for a couple of weeks, Van Gaal has been compared to Alex Ferguson, who was the master when it came to manager mind games.
Ryan Giggs said the new United boss had an “aura” about him – just like Ferguson.
Being compared to a man who won 13 Premier League titles with United has gone down well with the new man at the helm.
“I highly respect Alex because I don’t think there is another manager who has won so many titles,” Van Gaal added.
“I (have) won a lot of titles, but he did it in one club and that is fantastic and when you compare Sir Alex with me I am very proud.”
Meanwhile, Tom Cleverley admitted he is glad Van Gaal gave his “role model” Ryan Giggs a place on the Manchester United coaching staff.
Doubts were raised about Giggs’s future at the end of last season when he hung up his boots following a four-match spell as player-manager.
New manager Van Gaal brought five staff members with him when he was appointed in May, but he felt it was important to keep a link with the club’s past, so Giggs was immediately sounded out about becoming the Dutchman’s assistant.
Having been at the club for 24 years, Cleverley thinks the presence of the 13-time Premier League winner around the training ground can have a good effect on the squad this season as they look to challenge for the title following a dismal year under David Moyes.
“We have known [Giggs] for a long time and he is brilliant for the players,” the Manchester United midfielder said. “As a young player growing up at the club he has been the best role model there is.
“You look at his career and all the titles he has won and hopefully he can pass his knowledge onto the players. It is good to have him around.”
Van Gaal will take charge of his third match as Manchester United manager in the early hours of tomorrow morning in Washington DC.
Their opponents, Inter Milan, will have a familiar face in their 11 — that of Nemanja Vidic.
The former United captain joined Inter this summer after an eight-year spell at Old Trafford, where he amassed 15 trophies.
The Serb has settled in well at the Italian club and is happy to be working under manager Walter Mazzarri.
“He’s a coach who explains very clearly what he wants so it’s easier to do what he asks of you,” Vidic told Inter’s website.
United defender Rafael, meanwhile, will play no part in the game, or any of the remaining games in the club’s tour of the United States.
The 24-year-old sustained a groin injury prior to United’s 3-2 win over Roma in Denver and he has been sent back to Manchester for treatment.