According to Sam Lee of Goal, City have stepped up their interest in the Chile international, whose contract at the Emirates Stadium is poised to expire at the end of the season.
"The two clubs have held talks in recent days, and the Blues are cautiously optimistic of getting a deal done, despite the Gunners' £35 million asking price," Lee reported, with Arsenal said to be "resigned" to losing their No. 7 midseason.
Lee provided more details via his Twitter account:
City are said to be "unwilling" to part with that amount, although according to James Olley of the Evening Standard, Arsenal want £40 million for Sanchez.
Olley provided further details via social media:
James Olley @JamesOlley
Man City plan to make a concerted effort to buy Sanchez from Arsenal this month. Gunners holding out for up to £40m but suspect final fee would be less if they agree to sell. Depends on whether Wenger thinks it is worth hanging on for another six months. https://t.co/tItkTF4cP7
As Olley noted, clubs outside of England are able to negotiate terms with Sanchez directly with a view to a pre-contract agreement and a free transfer in the summer. Paris Saint-Germain are said to retain an interest.
Both reports suggest Gabriel Jesus' MCL injury has prompted City into accelerating a possible move for Sanchez. The Brazil international is set to miss two months through the problem, which he accrued during December 31's 0-0 draw with Crystal Palace.
City's interest in Sanchez has been longstanding. They failed with a late bid to bring him to the Etihad Stadium in the summer, as Lee noted.
Journalist Shane Burns feels as though the haggling will go on for a while yet:
Arsenal's position is unenviable. It appears almost certain they will be losing the forward, and if he does stay beyond the transfer window, they would receive no transfer fee for Sanchez at the end of the season.
It's why, as galling as it may be, the club may feel the sensible course of action is to take what they can in January and try to use the funds to improve the squad.
Still, Sanchez is such a talented player he could yet have a major say on Arsenal's season; while the Gunners were dumped out of the FA Cup on Sunday by Nottingham Forest, they still have the Carabao Cup, UEFA Europa League and a spot in the Premier League's top four to fight for.
Broadcaster Andy Goldstein believes Arsenal should keep the player because of his ability to conjure decisive moments:
While City are set to coast to the Premier League title—they have a 15-point lead over their nearest rivals—Sanchez could give them a huge boost in the UEFA Champions League.
Additionally, with Jesus set for a prolonged stint on the sidelines, Sanchez could help preserve the dynamism and fluidity that has been a trademark of the City attack in 2017-18.
While it's likely to drag on, you sense both sides will reach a compromise in this transfer window.