The 28-year-old has yet to be offered an extension to his current contract, which runs out at the end of the season.
The France international, who enjoyed a loan spell at Real Madrid in 2009, has said that he would consider a move back to his homeland should Sam Allardyce not match his ambitions.
"I would not mind going back to France if I don't get a suitable offer from elsewhere," The Mirror quotes Faubert as saying. "But for now I am concentrating on West Ham - it is a club I appreciate.
"I don't know if I will stay if we get promoted - that depends on the project and ambitions in the Premier League. I will not continue in the Championship - that is sure."
Faubert joined the Hammers for £6m from Ligue 1 side Bordeaux in 2007.