The 28-year-old looked set to be reunited with Pep Guardiola, whom he played under at Barcelona, only for his £60m move to collapse on deadline day after Arsenal failed to secure a replacement.
Sanchez has turned down an offer to extend his deal at the Emirates and the Gunners are resigned to losing him either in January or for free next summer, with the striker allowed to speak with foreign clubs in the New Year.
Earlier this month, reports suggested City would bid £20m for the Chilean as Arsenal appeared open to cash in on Sanchez rather than losing him for free at the end of the season, as Wenger conceded the Chilean and Mesut Ozil, whose contract also expires in the summer, may not last the full campaign.
According to the Sun, however, the figure is unlikely to impress the Gunners' hierarchy, with Wenger intent on securing a bigger fee for the forward, who scored 30 goals in all competitions last season.
"Arsenal are not blinking yet on Alexis," a source close to City was quoted as saying by the Sun.
We will only pay £20m for him in January. Arsenal are still sending the message that they want over £30m. Something has to give either way.
"Pep thinks he could prove the difference between Premier League and Champions League success and failure. Sanchez still wants the move from what we understand. We feel we have some leverage right now."
Sanchez made only his third Premier League start of the season last weekend, when he scored and provided an assist in Arsenal's 5-2 rout of Everton at Goodison Park, but Wenger has previously insisted the former Barcelona man remains an integral part of his squad.
The saga surrounding the Chilean took a new twist on Wednesday (25 October), when Arsenal majority shareholder Stan Kroenke confirmed that the north London club were still hoping to re-sign him and Ozil to new deals.
"We want to attract top players, keep top players. Those guys [Sanchez and Ozil] are top players," Kroenke told the Mirror ahead of Arsenal's Annual General Meeting scheduled for Thursday (26 October).
"I watched them on Sunday [in the 5-2 win at Everton] and they looked really good in black with the red trim. They looked really good and they played really well and we'd love to keep them.
"It takes two to dance. We'll keep working to keep our top talent and to attract more talent but some of the guys we've got are looking pretty good," he added.