The winger joined the Gunners on a season-long loan last summer after falling out of favour at Stamford Bridge but has struggled to make an impact in North London.
Sterling has scored only one goal in 27 appearances for Mikel Arteta’s side and is set to return to Chelsea when his loan ends.
"I think it’s time for a fresh challenge for Raheem Sterling, he has the chance to show what he could do at Chelsea and then Arsenal but it hasn’t happened,” Gallas told Genting Casino.
“He needs to go somewhere he will get more opportunities because even with some rotation at Arsenal, Mikel Arteta hasn’t given him that.
“I think one of Arteta’s biggest mistakes has been a lack of rotation at times because they have picked up injuries. You have to give players a rest at certain times, but with Sterling, he must be frustrated, maybe he will want to stay in the Premier League and in London.
“He’s 30 now, but maybe a club like Fulham could give him that opportunity and more chances to play. I'm curious to see what happens next."