Sanchez, who scored 24 Premier League goals for the Gunners last season, is out of contract next summer and has reportedly said he wants to play for City manager Pep Guardiola.
Arsenal have rebuffed all approaches for the 28-year-old and would like City’s Raheem Sterling as part of any deal before Thursday’s transfer deadline.
But Guardiola, who was in charge at Sanchez’s former club FC Barcelona, is understood to want the Chilean as a straight purchase.
England forward Sterling has featured in all three of City’s games so far this season.
However, the 22-year-old is not guaranteed a starting role at Etihad Stadium following the summer arrival of Bernardo Silva from Monaco.
Sanchez had joined Arsenal from FC Barcelona in 2014 for a fee of about £35 million and won the FA Cup for the second time last season.
Arsenal manager Arsene Wenger had said a few weeks ago that Sanchez would “respect” his decision and stay.
The Chilean made his first appearance of the season in the Gunners’ 0-4 defeat at Liverpool on Sunday, coming off for Alexandre Lacazette after 62 minutes.