The 33-year-old is currently with Chinese side Shanghai Shenhua after joining from Chelsea in January 2011 but has since become unhappy at the club.
Queens Park Rangers has also been reported as showing interest in the former French international, although it is believed Anelka would prefer a switch back to his homeland.
He played for PSG as a teenager in 1996 before rejoining the club 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.
Follow GOAL.COM on Twitter
- Sports & Recreation
- Shanghai Shenhua
- Real Madrid