The England midfielder - who scored his first international goals in the 3-2 win in Slovenia earlier this month - is a serious target for City this summer.
But, after years of financial constraints, the Gunners no longer have to consider offers for their best players.
Sportsmail understands City are undeterred by Arsenal’s stance, believing that a massive bid will convince them to sell.
The 23-year-old’s existing deal, worth £60 000 a week, expires in 2018 but talks over an improved contract will start in the opening months of next season.
Original source: Arsenal won't sell Wilshere