The Sunday Mirror says City boss Pep Guardiola will pursue Sanchez to the final day of the summer transfer window, despite Arsenal insisting that they will not sell the Chile international for any price.
Sanchez only has a year left on his Arsenal contract and is yet to put pen to paper on a new deal worth around £300,000 per week.
Paris Saint-Germain have also been linked with a move for the 28-year-old, but he is reported to prefer a move to the Etihad Stadium to reunite with Guardiola.
Sanchez played one season under Guardiola at Barcelona, with the pair winning one Copa del Rey together at the Nou Camp.
The Chilean forward is yet to feature for Arsenal this season as he is currently sidelined with an abdominal strain.
Asked about potential transfer business after Arsenal's 1-0 defeat at Stoke City on 19 August, Wenger said he expected some players to leave the club before the transfer window closes.
"I expect to sell players first, that is all," the Frenchman was quoted as saying by ESPN. "I expect some players to go because we have too many players and it is not manageable.
"Many clubs are in this situation which is why the transfer market is quiet. We have 33 players at the moment, and that is too many players."
Jese Rodriguez scored the only goal of the game at the bet365 Stadium, while the visitors had a goal disallowed and were denied a penalty claim.
"I am not in transfer mode after a game like that," Wenger added. "We are more disappointed at the moment rather than thinking about buying players straight away tonight."
Arsenal's next league assignment sees them taking on Liverpool at Anfield on 27 August.