The Gunners want in excess of £30m for the Chilean worldwide, despite knowing he will be free to walk away for nothing in the summer.
The Chile global has entered the final six month of his Gunners contract, and his representative is free to discuss a pre-contract agreement with a foreign side this month.
Sanchez has been a long-term target for City boss Pep Guardiola and the club saw several bids rejected for Sanchez in the summer transfer window.
City are also considering buying a centre-back in the transfer window, with West Bromwich Albion's Jonny Evans remaining a leading option, although ironically they could face competition from Arsenal for the Northern Ireland worldwide.
Former Manchester United defender Evans has been linked with a January move to the Emirates Stadium, with Manchester City also reported to be interested.
Although Wenger still insists there is no fracture in the dressing room.
Should a deal be done, Alexis will be eligible to play in the Champions League knockout stage for Manchester City, with clubs allowed to add one player who has competed in the Europa League to their squads.
I understand that Sanchez has again reiterated his desire to leave to Arsenal - and they are now ready to listen, and the player is hopeful that City can strike a deal this month, rather than waiting until the summer, when he can move on a free transfer.
The more likely scenario is that Man City will swoop for Alexis this month.