According to The Guardian, City will secure the services of the 28-year-old for around a fee of £50m.
Arsenal manager Arsene Wenger has been adamant throughout the off-season that Sanchez is not for sale.
However, Sanchez is in the last 12 months of his contract with the Gunners and if he does not sign a new contract, the Londoners could lose the forward on a free transfer.
Sanchez has already refused to sign a new contract which has alerted both Paris Saint-Germain and City.
Sanchez is currently on international duty with Chile at the Confederations Cup, with the nation through to the final of the competition after claiming victory in a penalty shootout against Portugal last night.
Chile will either face Germany or Mexico in the final on Sunday.