Faubert, 29, has left Turkish side Eskisehirspor and is now free to negotiate with interested clubs.
The player, who has been staying fit by training with Bordeaux, admits he is eager to return to France.
“I’ve always wanted to return, even if it did not happen last summer,” Faubert told L’Equipe. “I love Ligue 1! I have contacts with four clubs.”
The French newspaper claims Bastia and Ajaccio are two of the four clubs showing interest in the player’s services.
Julien Faubert was considered one of the most promising full-backs in European football when he joined West Ham from Bordeaux in the summer of 2007, but his career in England did not go as planned.
He even made two appearances for Real Madrid during a loan spell at Santiago Bernabeu, but was allowed to leave the Hammers on a free transfer in June 2012.
Faubert spent last six months at Eskisehirspor, where he scored 1 goals in 16 Turkish Super Lig appearances.