The 33-year-old, who began his career at PSG and also played for them between 2000-2002, has spent the last year with Chinese Super League side Shanghai Shenhua.
PSG Sporting Director Leonardo has played down talk of a return to the club, saying: "Anelka asked to train with us. We're available for him to help him maintain his fitness in the days to come."
"We did not think about (signing him). I do not think there's an opportunity," Carlo Ancelotti added in a news conference ahead of Friday's Ligue 1 home game against Ajaccio.
"He only asked to train. He played under me and we are friends now. I allowed him to train because of our friendship."
But rumours in France suggest that Anelka could be called upon by the Ligue 1 leaders if a disciplinary hearing involving Zlatan Ibrahimovic ends with the Swedish striker being suspended for stamping on an opponent's head in a fixture last month.
Harry Redknapp has also spoken of his admiration for the former Chelsea, Liverpool and Arsenal striker, and his interest in bringing him to QPR, though Anelka's wages, believed to be in the region of £10m a year, could prove a stumbling block - although there are also rumours that he has not been paid in full during his time in China.
- Sports & Recreation