The Gunners look set to sell captain Thomas Vermaelen to Manchester United in the coming weeks, with the Belgian having been a peripheral figure for some time.
Although Arsene Wenger is said to be ready to sanction the deal, he does want a new man to come in to replace the exiting ace, with Nastasic an option.
The classy Serbian defender barely featured for the Premier League champions last term due to injury problems, and could well slide down the pecking order with Manuel Pellegrini set to bring in £30m Frenchman Eliaquim Mangala.
City are thought to be ready to do business for around £16m, which Arsenal can afford despite splashing well over £40m to land Alexis Sanchez and Mathieu Debuchy.
The Gunners are understood to have been tracking the 21-year-old since his time at Fiorentina, and are attracted to his technical ability and versatility.
It remains to be seen as to whether or not the domestic rivals will be able to agree a deal.