City have been pursuing Sanchez for the entirety of the summer, but manager Arsene Wenger has remained firm on his stance that the Chilean will not be leaving despite only having 11 months left on his current deal.
According to Sky Sports, Pep Guardiola's side have lodged a new £50m ($64.6m) bid for the 28-year-old which Arsenal swiftly rejected.
The same report, however, claims the club are more open to a potential Sanchez sale if it meant Raheem Sterling heading the opposite way to the Emirates Stadium.
Sterling joined City from Liverpool in 2015 and has gone on to make 97 appearances in all competitions, but is expected to be a casualty on the bench if Sanchez was to arrive.
It was reported earlier that City would offer a Sterling-plus-cash offer for Sanchez. However, recent reports state that instead, Arsenal would have to pay a fee as well as sell their star forward in exchange for the England international while the Citizens remain committed to a cash deal.
Following Arsenal's 4-0 defeat to Liverpool on Sunday (27 August) where Sanchez made his first appearance of the season, rumours started circulating that he had submitted a transfer request, but the north London club denied it.
However, Chilean media T13 reported on Tuesday (29 August) that the former Barcelona player had asked to leave the Chile training camp to "conduct personal business" with time running out as the transfer window closes on Thursday (31 August).
Sanchez enjoyed his personal best tally in the 2016/17 season netting 30 goals in 51 appearances in all competitions, but could not help Arsenal do better than fifth place in the league.