The Citizens want the midfielder to help them fall in line with the FA's home-grown stipulations, which they failed to adhere to last season.
Wilshere's stock has risen recently after the midfielder scored two brilliant goals in England's 3-2 win over Slovenia in the Euro 2016 qualifiers, which all but confirmed their participation in the tournament.
Wilshere was also in fine form for Arsenal since coming back from injury, scoring a beautiful goal in the Gunners' thrashing of West Bromwich Albion in the last game of the season, winning the match 4-1.
The 23-year-old's career has been blighted with injuries but the midfielder is still an important part of Arsene Wenger's plans for the future.
The England international scored for the Gunners against City when Manuel Pellegrini's men visited the Emirates in the first half of the season. However, he sustained an injury soon after against Manchester United when a tackle from Paddy McNair saw him miss the next five months with an ankle problem.
City are likely to make a £30m ($47.8m) move for Wilshere in the next few days but are likely to be rebuffed in their efforts, with Wenger recently stating that their new-found financial stability allows them to keep their best players, which was not the case earlier.
The Citizens have gained from Arsenal's failure to pay huge salaries to their players by signing the likes of Emmanuel Adebayor, Kolo Toure, Samir Nasri and Gael Clichy over the years. However, Wilshere has repeatedly stressed his desire to stay at the Emirates and is unlikely to force a move out if Arsenal are unwilling to sell.
The midfielder was fined £40,000 ($63,665) by the FA for making and inciting derogatory comments about Tottenham from the crowd in Arsenal's open bus parade after winning the FA cup for the second year in succession.