I think Chelsea will be the biggest threat.
They have a good manager, a deep squad, and no Champions league to worry about. They will be a threat for the next two seasons before Abromovich fires Sarri and the whole Chelsea managerial cycle starts anew.
Both United and Liverpool over-performed last year. We're long past due for a Mourinho explosion regardless, I can't see him making it through the year. Liverpool punched way above their weight last year, and got injury-free and career years out of Firmino, Mane, and Salah last year. I wouldn't bet on that happening again.
Tottenham will be Tottenham. There will be a few months where they'll convince everyone they have a shot at a title, only to shoot themselves in the foot and finish 4th or 5th.
Arsenal doesn't have the talent or the squad depth. They're a cut below the rest. They'd do well to finish above 6th.