The 28-year-old has been heavily linked with a move to Bayern Munich, with the Bundesliga Champions keen to link the forward with his compatriot Arturo Vidal and push for a big run in the Champions League.
Goal reports that City's director of football Txiki Begiristain had travelled to London last weekend to hold talks with the player, but Arsenal have maintained that they will not sell to a Premier League rival.
However, it is reported that Sanchez is keen to link with Pep Guardiola, having previously worked under him at Barcelona, and City are willing to get the deal over the line by matching Bayern's fee and also providing him with a lucrative pay package.
The forward has been Arsenal's star player in the recently-concluded season, scoring 24 goals and assisting 10 in the league, but failed to lead the Gunners to a top four finish. However, Sanchez helped Arsenal win the FA Cup as he scored the opening goal in the 2-1 over Chelsea in the final.
City have already completed the signing of Bernardo Silva from Ligue 1 champions Monaco and are close to completing a deal for Benfica goalkeeper Ederson. They are willing to play the waiting game with Alexis, as they want Arsenal to do their bit in trying to sell the Chilean abroad should he decide to leave and later come in with an offer, which both parties cannot refuse.
The report states that City are also keen on the trail of Monaco's Benjamin Mendy and Kyle Walker as Guardiola looks to bring in atleast six to eight names next season in a bid to compete for the title.
The Citizens finished the recently concluded season in third spot, the first time Guardiola finished outside the top two in his managerial career.