United suffered a 2-1 defeat against relegation-threatened Sunderland on Saturday and missed the opportunity to close the gap on top-four clubs Manchester City, Tottenham, Arsena; and Leicester City, all of whom play on Sunday.
Their fading hopes of securing Champions League football have led to suggestions the club hierarchy has entered talks with Mourinho but Van Gaal said he would not reach out to the man who worked under him at Barcelona.
"I wouldn’t expect Jose Mourinho to call me about that," Van Gaal told reporters. "No. In the football world that doesn’t happen. Nor will I ring him.
"If I did, then you think the stories are right and it is not like that. I am not thinking like that."
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Van Gaal said before the Sunderland game that he would expect United to inform him if they were talking to other managers, such was his relationship with executive vice-chairman Ed Woodward, but appeared to backtrack on that claim after the defeat at the Stadium of Light.
"In the past, I was chairman of the coaches federation in the Netherlands and we had a rule that you can never talk with a club without informing the present manager," he said.
"But in football it’s not usual that you speak with other managers like that. It wasn’t a good rule, no!
"Sometimes it has been broken by people and by managers. It is always like that. It is not always an honest world."