The 33-year-old striker has been training with the Ligue 1 leaders and could be set to sign for the club for his third spell after becoming unhappy with life in China
And rumours of a switch to les Parisiens have gathered momentum after the striker began training with the club, though neither the player or coach Carlo Ancelotti have commented on the growing speculation.
The former France international played for PSG as a teenager in 1996 before rejoining them in 2000. He has also had spells with Liverpool, Bolton, Fenerbahce and Manchester City.
Anelka, who plays alongside his former Chelsea strike-partner Didier Drogba at Shanghai, has scored three times for his current side in 24 matches.