The Red Devils were not involved in the title race last season as the Blues lost out on the Premier League to Manchester City, finishing in third place.
Although Mourinho is full of admiration for the 62-year-old's managerial skills, he is not worried about Van Gaal reviving United as an additional title contender next season.
Mourinho told the Daily Mail: "I'm not worried about him being here. 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.
"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."
Chelsea face United on October 26 at Old Trafford in the first of their meetings next season.