Arsenal midfielder Ozil has also been linked with a transfer by Gallas, who played for the Gunners between 2006 and 2010.
Ozil has only made 13 Premier League starts this season – scoring three times and creating just a single goal.
Arsenal fans are unsure whether there is an issue between Ozil and manager Unai Emery – but Gallas has a theory that involves the 30-year-old.
“He only plays when he wants to play,” Gallas told The Sun.
The five-time German player of the year has been left out of six match-day squads in all competitions this season leading to speculation of a rift in the Arsenal team.
“Emery has tried everything he can to try and get a reaction out of Ozil but the player isn’t responding,” Gallas added.
“It is a very difficult situation for Ozil and for Arsenal.
“Everybody knows Ozil’s quality but he isn’t consistent.”
Gallas believes that Ozil has been far from his best even when playing this season, and thinks Arsenal may consider selling him in the near future.
He said: ”Ozil should be doing more with the quality he has, he has to be the best player for Arsenal every game that he plays in.”
“The fans are upset with Ozil and Emery knows this.
“If he doesn’t perform, Arsenal may consider selling him so they can use the money from the transfer and his big wages to buy a more effective player.”
Emery made Denis Suarez a deadline day signing and was forced to confirm that Ozil was still in his first-team plans.
“It’s no change for him [Ozil]. Suarez is coming here because we have a lot of problems on the wing,” Emery said.
“We haven’t got players to play right or left – that is the reason.”
Arsenal face a daunting trip north on Sunday as they take on Manchester City – the Gunners currently sit fourth, level on points with fifth-placed Chelsea.