Website Goal is reporting that the 28-year-old Chile international has made it clear to the north London side that he will not pen a new contract with the club.
Sanchez was heavily linked with a move away from Arsenal during the summer transfer window after he entered into the final 12 months of his contract at The Emirates.
Manchester City were the heavy favourites to land the attacker but a move failed to materialise despite Sanchez being linked with a deadline-day switch to The Etihad.
The same report says Sanchez has now made up his mind to leave Arsenal, and although Paris Saint-Germain are also believed to be interested, Manchester City remain as the favourites to land him
Sanchez would be able to sign a pre-contract agreement with a foreign club in January as the final few months of his current deal tick down.
The 28-year-old will be hoping to feature for Arsenal when the Gunners return to Premier League action after the international break next weekend with a trip to face Watford.
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