City bid £60m for Sanchez on deadline day in the summer, but the move fell through after Arsenal were unable to find a suitable replacement.
Sanchez's current contract at Arsenal expires at the end of the season, meaning he is free to talk to clubs and sign a pre-contract for next season from January 1 onwards.
However, according to the 'Daily Mail', Pep Guardiola is keen to secure the services of the Chilean forward in Januarym and will offer around £20m.
The Gunners did accept City's offer in January but their failed pursuits of PSG's Julian Draxler and Thomas Lemar from Monaco meant they weren't willing to part with Sanchez.
Guardiola also refused to let winger Raheem Sterling go to the Emirates in part-exchange for Sanchez.
Although £20m may seem like an extremely low offer for Arsenal's key man, Arsene Wenger may be tempted to cash in on the 28-year-old, given that he will otherwise leave on a free transfer in the summer.
Another factor which may make the move more plausible, is that it is looking likely that City will make the knockout stages of the Champions League in the New Year, whereas Arsenal will still be competing in the Europa League, having finished fifth last season.