Gallas' current contract expires in the summer and negotiations regarding fresh terms were recently put on hold by Wenger.
With the French defender struggling to play again this season after aggravating a calf injury, and the Gunners out of the UEFA Champions League, talks had been expected to resume.
However, Arsenal boss Wenger confirmed ahead of his team's game at North London rivals Tottenham on Wednesday that there was no update regarding Gallas' future at Emirates Stadium.
"No, there is no news," said Wenger. "There's no impasse and no agreement."
Gallas' fellow centre-half Campbell is also out of contract in the summer, having signed a short-term deal upon rejoining Arsenal in January.
Campbell, who will return from injury against his former club Spurs, has made nine appearances for the Gunners and no decision has been made regarding an extension.
Wenger added: "I don't know yet. I don't want officially to commit on that because I don't know what I will do.
"At the start he came to ask me if I could help him to get fit. Now he plays tomorrow against Tottenham. So that doesn't mean he has signed a contract for next season.
"Maybe he will not want to play, I don't know what I will want to do. At the moment we have short-term targets."