The Gunners contract rebel is set to become a free agent in the summer, but TransferMarketWeb reported a deal could still come to fruition in January (h/t Daily Star's David Wright).
The suggested figures would equate to a salary of £230,000 per week for Sanchez at the Etihad Stadium, although Paris Saint-Germain's supposed interest could throw a spanner in the works for City.
The Chile international was reportedly close to joining Pep Guardiola's side in the summer, but Arsenal's failure to sign AS Monaco star Thomas Lemar as his replacement saw the chase end. Gunners chief Arsene Wenger recently said there's been "no approach" for his player, via Goal:
Sanchez made a slow start to the campaign following the summer saga but is now firmly back in Arsenal's XI. He has started 14 of their 19 Premier League games, albeit with a far lower production rate than usual.
The 29-year-old has scored five times and made three assists in 16 top-flight outings this term, and Goal's Chris Wheatley felt his performance in the recent 3-3 draw against Liverpool was rather wasteful:
Reports of a contract being agreed between the player and Manchester City only count for so much, however, as the Gunners would need to agree a transfer fee to secure a January move.
Sanchez will be free to sign a pre-contract agreement with any non-English outfit next month in advance of a free transfer at the end of this season, but the Etihad Stadium is said to be his favoured destination, per Wright.
The Mirror's John Cross recently appeared on BBC 5 live Sport and reported that "PSG are the only other club interested," although he added waiting on a summer deal is an option for the Citizens:
That could end up being a risky manoeuvre, as it would leave Sanchez open to negotiate with foreign powers in the coming months.
In any case, the chances of the Chilean signing a contract extension at the Emirates Stadium look as slim as ever, and City still look like the team to beat.