Gallas also predicted that the Gunners will not win the UEFA Champions League this season as he also rate their chances of winning the FA Cup.
Arsenal are currently participating in the three competitions and will return to action against Southampton in the FA Cup quarter-final on Saturday evening.
They will also resume their Champions League campaign next week against Sporting CP in the quarter-final stage.
Mikel Arteta’s side will then face Bournemouth in the Premier League on April 11 after the Sporting game.
However, Gallas believes the Premier League will be the only title Arsenal will win this term.
“Can Arsenal win the treble? I think Arsenal will win one trophy and that’s the Premier League,” Gallas told football odds
“They still have to be careful but normally they would win the Premier League from this position.
“Champions League? I don’t think so. The FA Cup all depends on the result between Liverpool and Manchester City.
“If it’s Manchester City in the final, I think Manchester City will win. If it’s Liverpool vs Arsenal in the final, Arsenal will win. It’s a different style and I think Liverpool’s style suits Arsenal better.”