The Chilean has just 12 months remaining on his existing deal at the Emirates Stadium and with an extension now looking unlikely, Arsenal must decide whether to cash in or make him play out the remaining year on his contract.
Manager Arsene Wenger has previously claimed that his star man would not be sold to a direct rival in the Premier League, but it has been widely reported that Sanchez's preference is a reunion with Pep Guardiola, with whom he worked at Barcelona.
According to The Guardian, City are in no rush to force Arsenal's hand over the potential transfer, with an offer in the region of £50m said to already be on the table.
Arsenal continue to hold out hope that Sanchez will look to move abroad, but it has been suggested that City are confident of seeing off the likes of Bayern Munich and Paris Saint-Germain.
Regardless of where he plays his football next season, Sanchez is unlikely to be ready for first-team action until the middle of August at the earliest after he helped Chile reach the final of the Confederations Cup on Wednesday night.