The Chilean international will have just six months left on his contract come the New Year, meaning that he will be able to discuss a potential pre-contract with foreign sides.
The 28-year-old has been linked with the likes of Spanish giants Real Madrid in recent weeks, but is thought to be keen on a move to City, having seen a deadline day switch fall through in the summer.
English publication 'The Independent' reports that City will go back to Arsenal with one final 'big offer' in January in an attempt to bring in manager Pep Guardiola's top target.
Following their sensational start to the season, City harbour genuine hopes of completing a Premier League and Champions League double and are keen to reinforced their squad with players of Sanchez's quality in order to help them over the line.
Arsenal manager Arsene Wenger insists that the forward will not be allowed to leave the club in January, though City are confident that the right offer could convince him to change his mind, with the Frenchman having said similar in the summer, only to then open talks with City.
However, City will have to dig deep to get their man, with the aforementioned source reporting that Arsenal are likely to demand £50m for the player, despite him being available on a free in the summer.
Arsenal look resigned to losing their star, though they will no doubt be hoping that he opts for a move abroad, rather than a Premier League rival.