Etihad bosses have made contact with the Gunners to establish if a deal can be done in this transfer window.
City boss Pep Guardiola would like to bring forward his attempts to sign Sanchez after seeing Gabriel Jesus ruled out for up to two months with damaged ankle ligaments, as revealed in Starsport last month.
The Gunners could be willing to strike a deal at the right price, but will want to move fast to give them time to bring in a replacement before the transfer window closes.
City were confident of signing Sanchez on a free transfer in the summer when his contract expires.
The Chilean superstar has made it clear he wants to join Guardiola’s side instead of going to Paris Saint Germain.