Not much being rumoured at the moment, hopefully that will pick up in the coming weeks. For me personally I think we need to prioritise signings in this order:
1 - RB + RW. Equally. Like other posters have said, it's painfully obvious that our right hand side is weak again. Similar to 2010/11/12 where we relied on Baines down the left so heavily, we're almost at the same situation. Unfortunately some of this stems from the decline of Coleman although I think as a sub and for spells he's absolutely fine to start 10-15 games a season but he can not be our first choice for me. But we also need someone who can play RW just as desperately. Except for Richarlison who thinks he's a striker our wing options are poor, too poor if we want to be getting into Europe.
2 - CM. Dependent on if we decide we're keeping Sigurdsson/James then we'll need another CM in the Doucoure profile, someone who can TERN, take us forward and carry the ball - who importantly has the right physical attributes. It's so important that we had physicality to this team, we've seen how good the likes of Godfrey and Doucoure himself looked when they arrived because they're so ahead of the rest of our squad physically. A bonus would be a CM that can chip in with a few goals as well, this is easier said than done of course, but Davies, Allan, Gomes, Doucoure, added how many goals between them? (Not counting Sigurdsson or James as most of their goals came playing an attacking mid role).
Backup GK - Perhaps the easiest to fill, if we believe the media then Olsen is looking to come back, depends if the decision makers fancy it, personally I don't think he's a bad backup option and there's not much elsewhere so I'd be for it if we could get him for a few million.
Backup Striker - Difficult to do in summer until we get Tosun off the books, but if it's likely that Kean is going, a backup striker will be needed. I'd be happy to loan a more experienced striker if there's any possibility of that. I don't think we need to spend big here and I'd be happy keeping DCL on as first choice for another season to see if he can develop further. Having someone experienced off the bench and for injury cover/cup matches or simply to provide a different option would ease the pressure however, as long as that person is not called Josh or Cenk.
Bonuses:
LW - If we shift one of Bernard or Iwobi which I pray we do, investing in a LW to provide some more pace into the squad would be an unrealistic dream. We could easily get by without one of the two and without signing an extra winger, but if the right player became available at the right price I'd hope we'd pounce, similar to the backup striker I'd absolutely take a loan here if it meant a better player to help us push for a season (e.g. I would absolutely take Ivan Perisic on loan for the season if in any circumstances he became available - he wont.)
CB - Not sure what to make of Ben White links, but I'd think signing a CB as a marquee and first signing would be extremely negative (Although we do have a manager who plays that style of football). If one of Mina, Keane or Holgate were to go then I'd be for it, but for me I'd consider it a bonus and still hope that we'd target the first 4 player profiles first.
Jesus wept lads I need to give footy manager a break.