The Argentina international has been a bit of a disappointment following his €42m move from Palermo, and recent reports linked him with a move to Liverpool and AC Milan in the January window.
But Fenerbahce coach Ersun Yanal has declared his interest in bringing the playmaker to Turkey at the earliest possible opportunity.
"I asked to arrange an appointment in Paris to discuss the direction of PSG," Yanal told Turkish daily Fotomaç.
"Fenerbahce want to move forward with a real number 10."
The Le 10 Sport report claims PSG have already begun looking for a Pastore replacement, with the club willing to part with Pastore for around €20m.
Liverpool were thought to be interested in the creative attacker, with Brendan Rodgers looking to strengthen in January to capitalise on their strong start to the Premier League campaign. The Anfield club currently sit joint top of the table alongside Arsenal.
But AC Milan also present a viable option - Pastore played his best football in Italy with Palermo.