Anelka, 33, is currently locked in talks with his current club Shanghai Shenhua about terminating his contract.
Anelka moved to China 12 months ago, but things have not worked out and he has scored just three times for them and at one point was also player-coach.
But now he wants to move back to Europe, and the likes of Queens Park Rangers and West Ham United have both expressed their interest.
PSG's sporting director Leonardo has now confirmed that they are happy for him to train with them.
"Anelka asked to train with us and we are at his disposal to help him to remain fit when he will need it," Leonardo told L'Equipe.
Anelka began his career with PSG before leaving to join Arsenal in 1997 after playing just ten first-team games.