The 62-year-old, who will coach the Netherlands team until the end of the World Cup this summer, was officially confirmed as David Moyes's replacement on Monday.
After the news was made public, Van Gaal revealed on a Dutch chatshow that he received a congratulatory text message from Mourinho, who also said that he was envious of the coach's CV, which includes stints at Ajax, Barcelona and Bayern Munich.
"Mourinho congratulated me," said Van Gaal. "He was the first one I texted and he was the first one to text me back. He said he was jealous of my list of clubs.
"I didn't call Manchester United, I didn't call Bayern Munich, they've always called me, and I'm proud of that."