Don't think its going to happen on the final day but I am hoping it happens around their Liverpool game. But yea I think it will go down as you describe it.
City will bid maybe 35-40m, and brief the press about it.
Arsenal will reject.
Sanchez will hand in an official transfer request.
City bid 50m.
Arsenal stall and eventually accept.
Sanchez holds up the number 9 shirt with a great big smile on his face.
Pretty standard, Sanchez is seen as the enemy, Arsenal get their money and buy a replacement, everyone is happy.
I know Pep & City would prefer it goes down quietly but lets be real its not going to happen like that. The fans would revolt, Arsenal have to make a big scene out of this and we'll get the expected statement from Wenger: "We had no choice but to sell Sanchez." The fans will direct all their hate at Sanchez and continue to support their club.