Mourinho, who takes his unbeaten Blues side to Old Trafford in the Premier League this afternoon, has previously spent time working under Van Gaal at Barcelona.
Both managers have enjoyed success at numerous clubs since then, and Van Gaal believes that there are a lot of similarities between himself and his opposite number.
"I have a relationship with every person I meet. But he is special," the Dutchman is quoted as saying by BBC Sport. "I knew him when he was my assistant. He had to analyse all the matches and he came every week to my house to explain so I know him very well.
"The respect and confidence grew and when you have that in people it mostly ends in friendship. I think what I see in his teams is the same as I do [in mine]. But he is further in the process - you can see that - but we can win today."
Follow Sports Mole's live coverage of the action at Old Trafford here.