The versatile Frenchman, who can play at full-back or in midfield, joined Bordeaux in January on a deal until the end of the season after being released by Turkish club Elazigspor.
It was his second spell at the club, having played for Bordeaux earlier in his career before heading off to West Ham United and having a short loan stint with Real Madrid.
Faubert performed well enough for Bordeaux during the second half of last season for the club to decide they wanted a new deal to be agreed, and it is now set to be finalised.
"We found an agreement," he said in L'Equipe. "It is just a matter of hours or days."
Faubert, 29, is expected to sign a two-year contract.