I see Sané myself even if only at Newcastle or if he spokes at Aston. All other top clubs have no need in his position and not for a 29 year old with such salary requests. And I think the frequently mentioned names like Chelsea and Arsenal are completely unrealistic. Chelsea uses younger players and is not really needed and if you get a winger, this will certainly be more of a gitten. Arsenal is more than well occupied with Saka, Martinelli, Trossard, Sterlin, Nswari and G.Jesus (when an MS comes).
Newcastle has no need in front, they buy in other regions anyway.
Aston Villa cannot afford Sané in terms of salary, whose sales personnel cost quotient is terrifying even for PL conditions and I assume that the Rashford wants to commit, which will cost considerably.
To Arsenal: Sterling is back at the Payroll of Chelsea in 2 games – thank God. Jesus is out until the end of the year and whether he will come back again, I have my great doubts.
Saka and Kai paid the award this season that they had to play almost every game for the past 2 years, they are so indispensable. Also because the squad width is a problem, for example that Nwaneri had to play the right wing for Saka. If he did well, it is just not his position, but it comes from the middle and would actually be the ideal backup for boring. For Saka, Arsenal has no real backup at all, on the left Martinelli and Trossard alternate, but this year is also not very productive. And both are always mentioned whether something will not happen on the departure side.
Sané would be an enrichment with the Gunners, just a squad player instead of the to-go-Guy, but: Mikel knows him from city times, he can play on the left and right, also to relieve Saka, which would at least be closed.
If the framework conditions are right, I could already imagine it with us, i.e. a similar contract as Bavaria offered it. Especially not over 3 years.
A new striker will certainly come, probably Gyokeres, and Zubeni is traded. Both would be set, just like Rice, Ödegaard, Saka and Martinelli. Accordingly, people like Merino, Havertz etc would only be a rotary player anyway. G.Jesus is scheduled to come back on November 22nd, after that the season is still very long and up to this point there is no major rotation.
Then the question is who would buy Martinelli or Trossard for a lot of money. And then a loan is rather unlikely. And if you give up one, a regular candidate would come, in which I don’t see Sané, just like you.