The Gunners are reluctant to allow their star player to join a Premier League rival and will only consider a significantly higher offer from Man City if they are to sell before the end of the transfer window.
However, City are determined to get the deal done before Thursday's deadline and will return with another bid in an effort to convince Arsenal to allow the Chile international to leave.
Arsene Wenger would reportedly be interested in any deal which would see either Raheem Sterling or Sergio Aguero move in the opposite direction, although City are eager to keep it as a straight purchase.
Sanchez himself is understood to be keen on the move in order to play Champions League football this season and reunite with former Barcelona boss Pep Guardiola.
However, Arsenal have repeatedly insisted that the 28-year-old will not be leaving the club this summer despite entering the final year of his contract in North London.