I've been thinking about this a lot for the past couple of days for some reason, and the list of players who could theoretically leave is quite high. Obviously, I don't expect us to have a major clear-out, as this very rarely happens even when you have a lot of players most would consider 'average'. Normally even in a busy Summer, you'd only lose 4-6 players at the most who were considered part of the 23-man squad (roughly). Here's who I think is in danger of being given the boot, or in some cases, who we're in danger of losing (you can probably add any of the CB's bar Bailly to this list as well, if we sign another one):
Matteo Darmian
David de Gea
Zlatan Ibrahimovic
Anthony Martial
Wayne Rooney
Bastian Schweinsteiger*
James Wilson
Ashley Young
Basti has already gone, and obviously Memphis/Schneiderlin left already as well which starts to make a potential big list. I think Darmian will be surplus to requirements along with Wilson who is too injury prone. I have grown to like Ashley Young more lately, but I think his wages are still too big to warrant to the role he is playing for us. Rooney will likely go to Everton, but I think he may be tempted to try and fight for a place if we're in the Champions League (which is probably why he hasn't made a decision already).
Now, with those out of the way (losing roughly six squad players and a youngster or two in half a year), we move onto the big questions. Will Zlatan stay another season? Champions League may be a factor here, as he might want one more season in it before he decides it's time to settle for something a bit more 'small time' in comparison to his previous clubs. If Dave wants to go to Spain he will, and I don't think anyone will blame him. Up until now, he has probably been too good for us if I'm honest. We're lucky we kept him through the LvG years. Martial is a tough one, but it is guaranteed we sign a forward of some distinction and there will be a lot of competition across that front three. It seems like Martial wants to be the main striker of a team, or at least guaranteed to start as one of a front two or three every game, which is hard for anyone in our squad.
I think Griezmann is coming regardless of if we lose Zlatan/Martial, he'll be more of a replacement for Rooney (but actually start every week). Other than that, I can't see who else we will get... If Jose trusts Shaw / Fosu-Mensah to play full back then he might resist buying one. Again at CB, if he doesn't sell one of Jones/Rojo/Smalling, I don't think we'll sign one. Central Midfield is guaranteed to have a major signing, though. If we lost both Zlatan and Martial, then I could see us paying out for Lukaku as well, but I do see him as a major target for Chelsea - buying back players you sold seems to be a thing these days.