I don't think Griezemann and Mahrez are likely to want to play for us. I know Griezmann is a United fan but what they are building at Atletico is marvellous- their team is already great, and will only get better. Surely you'd rather spearhead a great team's attack rather than our currently bad one? But would honestly love him here. Mahrez could go to Barca if offered, and he is in a team that is better than United already.
Mhkitaryan, again logically speaking, why leave a team that is inferior to yours? Potentially attainable but wouldn't bet on it. He is a great player though, but I thought his best games have come at #10? Not sure, I don't watch them.
Payet, Dembele, Willian could all be likely. But Payet is 29 and he is #10, a position that we have too many players for. Dembele is a really good talent who could go to most of Europe's top clubs, it is possible he could join us but I am not so sure (again, would bloody love him though). Willian, I feel, would rather see how it all is under Conte. Again it is possible though.
Mané's best performances have been at #10, once more we don't need any more players in that position.
Leaves us with Yarmolenko and Sané, both of whom are attainable and we can definitely pay for them. Out of those two I'd personally sign both, purely because we basically have no impact subs.
EDIT: Just realised you didn't mention Griezmann, my bad. But the point still stands and many have said we should go for him.