The Gunners have been resistant to all approaches, but City are ready to up the ante with the £60m bid, and by offering Sanchez an incredible £400k-a-week wage packet.
The Chile worldwide could run out his contract at the Emirates with less than 12 months left on it.
Wenger has insisted several times that Sanchez will not be sold, although links with Manchester City continue.
The Gunners have looked like trying to replace him by targeting the likes of Kylian Mbappe and Thomas Lemar this summer, but neither deal has come to fruition.
Paris Saint-Germain and Bayern Munich have previously been linked with moves for the Chile global, but it seems that Manchester City are leading the chase amid reports that Pep Guardiola's club are preparing a £60m bid.
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Arsenal are also confident now that Sanchez will stay for the final year of his contract - and have not given up on him signing a new deal.
But Sanchez wants out of Arsenal ASAP after they failed to qualify for the Champions League and Man City and PSG expressed interest.
While Arsenal won just their second opening fixture in the last eight years, they were pushed all the way by the Foxes, who had led twice during a frenetic evening at the Emirates Stadium.
Tweeting from Paris, France - the location of Ligue 1 giants Paris Saint-Germain who have been linked with a move for the forward - hasn't gone down too well with the Arsenal faithful as they fear last season's top scorer could be on the move.
Sanchez is now in the previous year of his current contract and negotiations regarding a new one have reportedly stalled.