It is understood Arsenal are demanding £35m for the Chile international, while agents are likely to receive another £5m on top, totalling a £40m deal before the player’s potential wages are taken into account.
The Premier League leaders are understood to be unwilling to go beyond a £20m fee for Sanchez, given there is a chance they could get him for nothing when his Gunners contract expires at the end of the season.
With Manchester United also interested, City are prepared to risk losing out on the player altogether.
City believe Sanchez is keen to join them and link up with manager Pep Guardiola for a second time, following their successful spell together at Barcelona.
Sanchez is keen to leave Arsenal in the current window and Gunners boss Arsene Wenger appeared resigned to losing him in his pre-match news conference on Friday, ahead of Sunday’s trip to Bournemouth.
Arsene Wenger acknowledges Arsenal will not let Alexis Sanchez leave until a replacement is signed.
But he said, “A bidding war is always beneficial to the club who can take advantage of it, but we are not in that.
“It’s not that I don’t want to inform you. I don’t want to give you wrong information. At the moment, nothing is decided one way or another.
“I maintain what I said. Many times, that normally he should stay here until the end of the season, but we will see.”