Liverpool and United probably. I think Spurs may have peaked. The way Levy operates and the wages they pay, means they've been relying a lot on the idea of being part of a project alongside young exciting players that will win trophies. I think you can only sell that idea for so long and if the trophies don't arrive quickly then their biggest names are going start leaving for market value wages and actual trophies. The fancy new stadium will probably give them a 1 yr grace period with some of those players but after that they're their chance has gone.
Liverpool will be vastly improved if they bring in a new keeper alongside Keita. However, there's a possibility their fundamental flaws will remain. Get carried away after beating a top side and then lose to a shit one. We'll also find out for sure next season whether the problem has been their defenders or if it's simply that Klopp can't defend (hopefully the latter).
United have spent a lot of late and have a massive wage bill. Can't see any marquee signings coming in. I guess they'll strengthen but then again, so will we. After the stick they've had this season and given they've looked better when they take the game to teams, maybe Mourinho will take the handbrake off next season and it will make them more of threat. That said, it will take some getting used to and there could be slip ups along the way. There's also the potential for unrest as I can see the Pogba situation continuing to deteriorate.
Arsenal will improve but they're not ready to challenge and Chelsea will be in a season of transition with probably a new manager, new stadium and potentially without Hazard and Courtois.
As for us, we have a head start on everyone else and will also strengthen (though there isn't much room for improvement broadly speaking, it's just a case of maintaining that consistency.) Given Mendy has been out virtually all season, we'll essentially have a top player coming in to strengthen at LB and hopefully Laporte will settle in. Sane and Bernardo will continue to improve and hopefully Jesus will hit his stride. Then we'll bring in a couple on top of that.
It will be harder next season but we should be favourites.