The England worldwide is open to joining Arsene Wenger's side as he could fall down the pecking order if Sanchez arrives.
City have been strongly linked with a move for the Chilean global all summer and it seems they've now stepped-up their interest by opening formal talks with Arsenal.
Arsenal supporters' rage at the club would be amplified even more if they made a decision to sell star man Alexis Sanchez to a rival before Thursday's transfer deadline.
Sterling has been in-and-out of the Citizens lineup since the start of the season, but he has still proved effective with an equaliser against Everton which was followed by a late victor versus Bournemouth.
However, they would be willing to negotiate if winger Raheem Sterling is included in any deal, as well as if City offered them a huge sum of money.
Sanchez was in action on Saturday in the Arsenal's humiliating defeat to Liverpool at Anfield.
The Chilean worldwide made his season debut for Arsenal on Sunday, and he was hardly a factor in the 4-0 demolition the team suffered at the hands of Liverpool.
Chilean newspaper La Tercera reported on Tuesday that Sanchez asked national team coach Juan Antonio Pizzi to be given some time off on Wednesday in order to deal with some "personal formalities". Especially as Wenger risks losing him for free next year.
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