Moyes also expects a big threat from Manuel Pellegrini's Manchester City.
"I think there will be improvements from all of the clubs. I am really pleased to see Jose (Mourinho) back, he is someone who everyone will enjoy working in this country. He has been very successful and I think we will enjoy having Jose back in the Premier League again," he said.
"I have come across Manuel Pellegrini a couple of times at Villarreal and Malaga, so it will be new to him as well. Probably for the first time there has been quite a big shake-up in the Premier League and because of that I think there are a lot of things unknown, how things will pan out. I don’t think it’s just at this club, I think there are a few other clubs where it is similar."