Cleverley, 23, reckons United will need to keep an eye on more than just Manchester City this term.
He told The Sun: “The way the four teams have started you can definitely see a four-horse race.
“Arsenal are probably playing the best stuff at the minute while Chelsea are winning games — which is what they are good at.
“It’s dog eat dog up there. You know if you get a bad result there’s going to be two or maybe all three of the other teams winning.
“You have to be on your game every week and a bad three or four-game run could be very significant. I think it will be the most competitive season ever.”