Wenger has made clear that his preference is to remain at Arsenal but is facing mounting protests from supporters after four defeats in five games, the worst run of form the club has endured since 1995.
Gallas captained Arsenal between August 2007 and November 2008, leaving in the summer of 2010.
Though the 39-year-old did not always enjoy the strongest relationship with Wenger he is convinced his former manager will want to stay to ensure his reign does not end at a low point.
“He will want to stay,” Gallas told SFR Sport. “He loves this club. He has been there for 20 years. He wants to win titles.
“He has not won in a long time but (his stubbornness) shows his passion. He will not want to finish on a failure.”
Wenger also insisted this weekend that his future would not be dictated by whether Arsenal managed to qualify for the Champions League this season – they are six points off fourth placed Liverpool with two games in hand – saying that he was taking a “bigger perspective” in deciding on his future.