The 25-year-old has come into criticism following a series of under-par performances for the reigning Premier League champions this term, and has been largely disappointing since arriving at the Etihad Stadium from Arsenal in the summer of 2011.
Citizens boss Roberto Mancini recently singled Nasri out for individual criticism, and is now believed to be considering selling the French flop when the transfer window reopens in July.
PSG boss Carlo Ancelotti has been credited with an interest in signing the former Gunners star, who left the Emirates Stadium in acrimonious circumstances less than two years ago.
Nasri's agent, Jean-Pierre Bernes, recently claimed his client would stay and fight for his place at Manchester City, but a chance to move to Parc des Princes might turn the player's head.
Whether the Premier League side will accept a cut-price offer from PSG remains to be seen, with the capital club's known riches following recent Qatari investment, meaning City could hold out for a bigger fee, as they look to recoup as much money laid out on Nasri as possible.