Van Gaal will be desperate to improve the Red Devils after a poor season last time out and he is hoping to battle the likes of Chelsea and Manchester City for the title.
Mourinho has deep respect for his new counterpart but believes they are both great coaches.
“I’m not worried about him being here. I look forward to playing against United. Nothing worries me,” Mourinho said.
“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.”