Arsenal boss Arsene Wenger is determined to keep his star forward, despite no new deal forthcoming.
The Chile international could run out his contract at the Emirates with less than 12 months left on it.
And Wenger has remained insistent Sanchez will not join a Premier League rival this summer.
However, City are still looking to add the former Barcelona ace to their ranks.
According to The Telegraph, City will test Arsenal's resolve by putting in a £60m offer before the window shuts.
It is said Pep Guardiola is desperate to reunite with Sanchez, having worked with him at the Nou Camp.
And the manager is forcing City to table a bid to Arsenal.
The Telegraph add City are also prepared to pay the 28-year-old £400,000 a week, including bonuses and image rights.
But they must first convince Arsenal to sell.
Sanchez is set to sit out Saturday's trip to Stoke through injury, leaving some fears among fans he could still go.
While City are keen, Paris St-Germain have cooled their interest, and Chelsea believe a pursuit is worthless.
Sanchez ideally wants to leave this month but is prepared to wait and go on a free transfer next summer if he has to.
Should City make an official bid, Sanchez may push for a move, though.
The Chilean has been at the Emirates since a £35m move from Barcelona in 2014.
