Ok let's see what we have and I can add something into this as a part of a brainstorming. It will be a fantasy at the end.
Pickford, Stekelenburg, Robles
I would stick to Pickford as he has shown some signs that he can be the one here. Stek is old, don't think he'll ask for a move due to lack of first-team chances so good sub in any case. Robles is a huge disappointment, doesn't matter either he moves or stay. He can be replaced with a young GK.
Keane: In my country, we have an idiom (or maybe a lay terminology) for the people like him. The boy is clever but not making any effort so he looks like a dumb. I think it fits him. Got potential, doesn't give a damn, inconsistent. Can't trust him.
Jags: Consistent, gives all he can under any circumstances. He is so old now, can't trust him again next year, good as a sub tho.
Williams: I'll not even honour him by giving a comment.
Holgate: Good as a sub, he has a potential but more as a CB than an RB.
Funes Mori: He needs a mentor who can let him focus on his skillset. In normal conditions, he is a good enough CB for Everton IMO, either as a starter or a sub.
Sign at least one proper CB.
Baines: What a left back he was in his prime. He still can be useful but as a sub. Can't trust Martina or Garbutt.
Garbutt: A big question mark for me but obvious that he can't be trusted. 2nd or 3rd option.
Definitely needs a starter addition here.
Coleman: He is still good enough. He can handle RB as a starter.
Jonjoe Kenny: Loan him out. He needs experience.
Cuco Martina: Free transfer. He can remain in the squad as a 3rd option RB.
I would dig the market for a 2nd option RB. 27-28 years old one maybe, until Kenny develops himself as a better RB.
Morgan: He is not giving his 100% for a reason, don't know why but he is a good midfielder. I think he needs to be more focused than he'll start performing. He deserves at least 1 more year.
Gana: I think he has some skills but I find him a very risky option because of his lack of positioning and passing abilities. He is a living and walking example of a Pros/Cons chart. He is not the major problem of the squad so, maybe he can perform better under another manager with a different set of tactic.
Needs 3rd option, can be covered up in the squad or from the youth team.
McCarthy: Not sure when he'll be recovered from his injury but I want to see him healthy and what he can offer.
Beni: I would loan him out next year.
Davies: He has a huge potential. Loan him out to a Championship side or a lower Premier League side. He'll be way better after some years but he needs to play consistently in a challenging league.
Rooney: A good sub or he can leave. His legs are crying for help, still a passer but not enough alone.
One more experienced midfield who has stamina while youngers still developing would be great.
Davy: He deserves more chances. He used to be a promising one, quality. He can offer more with a better treatment.
Gylfi: One of the best players in the current squad. He'll be more effective as an Attacking Midfielders instead of Left Wing.
Bolasie: Sell him for any price while you still can, probably it'll be less than what you paid but at least save some from your loss. A still living headless chicken.
Vlasic: Needs experience either as a sub or as a loaned player. I would keep him as a sub.
Lookman: Trust him, let him show what he can bring to the team. If he is not a good starter, use him as a sub.
Walcott: He'll be good enough.
Sub here, please.
Tosun: He'll never be the 30 goals a season guy but as I mentioned in another topic, he can bang 15-20 in a season with a proper service. He is not so effective outside the box but he is good inside the box. He is good with link-up plays, he can switch positions to create surprising attacking sets. He has a skill set, it is up to the manager to use his tools. Depending on that, he can be a huge disappointment or a success.
Niasse: He can have a spark in tired opponent defenders' asses. He is definitely not a starting striker in any case but a super sub for the second halves.
DCL: Not good enough for this level yet, doubted but still hoping he'll be in the future. Loan him out for more experience.
Sandro: Bye bye darling.
Onyekuru: I don't think he is there yet. Keep loaning him out.
Mirallas: I don't think even Olympiakos will use their buying option. Sell him whatever price. Get rid.
Besic: Not sure about him.
Galloway: Not sure about him either.
Priority for me as below;
CM - CB - LB - LW