The Blues boss says he is looking forward to going head-to-head with the Dutchman in the Premier League and is backing him to do a good job at Old Trafford
The duo know each other well having worked together for three years during their time at Barcelona and Mourinho says he is looking forward to facing the Red Devils in the Premier League this season.
"I'm not worried about him being here," he told the Mail on Sunday.
"I look forward to playing against United. Nothing worries me. I watched him at his press conference and he was pure Van Gaal - honest and open, the way he always is."
Van Gaal has won titles with Barcelona, Bayern Munich and Ajax during his career and Mourinho is backing the Dutchman to do a good job during his tenure at Old Trafford.
"He is a very, very good coach, he'll be great for Manchester United. We are both great coaches.
"It's what we were born to do. Louis was the best coach in the World Cup and he is a good friend - really, a friend for life.
"I have deep respect for this man. He is in the best period of his career. With coaching, if you deal with winning and losing in the right way, you improve.
"He analyses every experience. He has got better and better."
Mourinho will likely get his first chance to test himself against Van Gaal when Man Utd host the Portuguese's Blues on October 26.