The Manchester Evening News has reported that Barcelona are lining up a move for the Spanish international following the departure of Pedro to Chelsea.
The daily newspaper state that Navas has been pushed down the pecking order at the Etihad following the arrival of Kevin de Bruyne from Wolsfburg earlier this summer.
Turan is unable to play for Barcelona due to a FIFA imposed transfer ban however, the 28-year-old played an hour of football against the Dutch on Sunday. Barcelona will be able to register players once again in January 2016.
The 28-year-old has now scored twice and provided two assists in his last three Euro 2016 Qualifying games for Turkey.
Turkey take on Iceland and the Czech Republic in their next two Euro 2016 qualification games.