The attacking midfielder has won two Premier League titles and a League Cup with the Citizens since arriving from Arsenal four years ago.
In that time, he’s made 170 appearances across all competitions – but injuries reduced him to just twelve Premier League outings last season.
The France international appears to be surplus to requirements at the Etihad Stadium.
Pep Guardiola excluded Nasri from pre-season and didn’t call upon the 29-year-old during City’s first two Premier League fixtures of the 2016/17 campaign.
According to The Daily Mail, Turkish champions Besiktas are hoping to hold talks with the Premier League title hopefuls regarding the former Marseille man.
Meanwhile, Napoli have asked about signing defender Eliaquim Mangala on a season-long loan. Valencia and AC Milan are also said to be interested in the 25-year-old.