The Frenchman is in the last season of his current deal at the club and he looks set to leave.
There is little appetite to offer him a new deal at the Emirates at the moment and Football Londonreports that the striker is also not thinking about signing a new Arsenal contract.
However, the attacker showed in the match against Palace that he might still have something to offer.
With Arsenal heading for a 2-1 loss, he entered the match and changed their gameplay.
He caused all kinds of problems for the Palace defence before eventually getting a goal to help the Gunners earn a share of the spoils in a 2-2 draw.
Despite that performance, former Aston Villa striker, Agbonlahor, still believes the Gunners should get rid of him because he struggles when he plays from the start.
Asked if Arsenal should keep the former Lyon man, Agbonlahor told Football Insider: “I would get rid of him.
“Lacazette comes on and gets the odd goal but when he starts, he does nothing.
“It’s alright coming on and geeing up the fans and doing this and that but since he’s been there he’s not been good enough.
“He doesn’t score enough goals as an Arsenal striker given what they’ve had in the past.
“For me, I would replace him and get someone younger and better in.
“You start Lacazette in the next game and he probably won’t score or even have a decent game. When he comes on he might have a little impact.
“The goal he scored [against Crystal Palace] was not a difficult goal to score, it was a tap in.
“Arsenal need to change quite a few players in that team.