I think you have far too much competition for him to stay unless you shift 2 or 3 players. With a fully fit squad you’d say that Pogba, Fernandes, Rashford and Martial are pretty much certainties to start so he’s competing for a RW spot (James, Chong and seems like you’re interested in purchasing someone else) and as backup for Rashford/Fernandes/Pogba in the LW/CAM spot.
By all means he is highly rated on here but I’ve not seen much yet at a senior level. Lampard does want to build a youthful side full with English talent though it seems so wouldn’t be surprised if that interest is true.
But we should shift those players!
Rashford-Martial-
RW (Greenwood, James, Ighalo)
---------------Bruno-------- (Gomes)
-----------Pogba----------- (Fred)
---------------
DM------------- (McTominay)
LB--------------WanBIssaka (Shaw, Williams)
------Maguire-
CB-------- (Lindelof, Bailly)
-------------De Gea-------- (Romero)
Lots of time for Gomes, Greenwood, Williams and James with Dalot and Henderson on loan. This is what Bayern or Madrid would do. Quality 18 or so first team players (say the first team then 2 attackers (one #9, one wide) 2 mids (one box to box and one holder), 2 defenders (one center back and one fullback) and a keeper) then 3 or 4 youth getting the rest of the minutes and hopefully one or two break into that 18 in a year or two. If Gomes is a disaster then when Bruno or Pogba are out you play Fred in a 4-2-3-1 or start James or Greenwood and play 4-4-2 or even Lindelof with 3 at the back.
Point is, Gomes is the kind of promising young player at a position we are short of numbers at. Not sure why he'd leave, unlike someone like Laird who now has 3 young players ahead of him at RB in AWB, Dalot and Williams.
Chelsea makes no sense, they have Mount and Loftus-Cheek and also can play Kovacic, Kante and Jorginho together and if Hudson-Odoi is also healthy then Pulisic and Ziyech would be ahead of Gomes centrally as a #10. I guess they could sell Barkley and end up like this in midfield:
Mount (Gomes)--------------------Kovacic(Loftus-Cheek)
-------------------------Kante(Jorginho)------------------------------
but that still leaves Gilmour looking for minutes and he's had better first team appearances than Gomes.
If he went to Ajax or Real Sociedad or Borussia Moenchengladbach or Porto or some team that has a hole in attacking midfield or might be about to have one (hence Ajax with Van De Beek and Sociedad with Odegaard) I would understand that, or even to Arsenal or where he might win the #10 job with a strong few weeks in preseason then sure, I would understand.