The 28-year-old is out of contract at the end of the current campaign and has refused to sign a new deal, while his attempts to force an exit from the club over the summer proved fruitless.
A deal involving Sterling could hold the key to Sanchez's future as Wenger could then be prepared to sanction a transfer for the Chilean star to recoup some money before he becomes a free agent in the summer, as per the Mirror.
The Chile worldwide is set to leave the Emirates next year with his contract expiring at the end of the season.
City tried to get Sanchez in the summer but had a final bid of £60m rejected.
Sanchez and City were left reeling at the failure to get a deal done, but they left it knowing that their interest would be resurrected in January.
And Gary Neville has appeared to endorse the move by claiming his former club should always be trying to sign "the best players in the world".
"Sanchez has been distracted at Arsenal for the last six months". "His career at Arsenal, I couldn't say a bad word about him until two or three months before the end of last season".
The Citizens have started the season in devastating form thanks in large part to the performances of Sergio Aguero and Gabriel Jesus.
It is said Arsenal are likely to get offers in January for their wantaway star.
City are still believed to be interested, while recent reports suggest Manchester United are ready to battle their city rivals for Sanchez's signature. Sanchez wasn't on the pitch; Alex Iwobi and Danny Welbeck were playing [up front].
"Sanchez has always been a hard worker".