Sanchez, 28, has less than 12 months left on his current contract at Arsenal and is yet to sign a new deal.
The Chile international has already rejected a £300,000-a-week offer from the Gunners to extend his stay as he wants £400,000-a-week.
He was on the verge of joining Manchester City on transfer deadline day after the north London club accepted a bid totalling £60million.
However, his move was blocked at the last minute after Arsenal failed to get a deal over the line for Monaco winger Thomas Lemar.
Alexis Sanchez returned to action for Arsene Wenger’s side from the bench in the 3-0 win over Bournemouth on Saturday.

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And he was welcomed back to the Emirates by boos from a section of the fans.
But despite the debacle over his proposed transfer, Wenger revealed he held clear-the-air talks with the forward when he arrived back from international duty with Chile.
The French boss also dismissed former Chile Under-20 coach Jose Sulantay’s claims that Sanchez is ‘fatter than normal’.
“Yes, I spoke to him. He is focused, he told us he is focused on the Premier League and Europa League. On top of that he had a bad result with Chile against Bolivia, but he came back full of desire and ready to play.
“He was not completely physically ready to play three games in a week – and for Chile he was not completely ready.
“He is not fat. His fat percentage is under 10. You know how it is, when you do not win, people will find problems.”
Up next for Arsenal is a Europa League clash with FC Koln on Thursday (8:05pm).