The Gunners boss has come in for increasing criticism in recent weeks after a poor run of form has seen them fall out of the title race.
A number of fans are now calling for him to be replaced as manager, believing that a change of boss could turn them into genuine contenders once again.
Who would replace the Frenchman has caused similarly fierce debate though, with many questioning if there is a coach of the required calibre available to replace him at the Emirates.
Savage though, believes that the answer could already be in the Premier League in the shape of manager Ronald Koeman.
“You've always got to think, if he was not to be the manager, who could be his replacement?" he told BBC Radio 5 Live.
"I look at Ronald Koeman at Southampton. I think he's a fantastic, young manager with great ideas who plays great football.”
"So I think there are replacements out there for Arsene Wenger."
Who could replace Wenger at Arsenal is certainly an interesting debate given the lack of top-level coaches currently available.
Koeman is not at that standard yet, but has shown during his time with the Saints that he can be a top coach.
His side play attractive football to say the least, and have done so for the entirety of his reign, while his work in the transfer market is not to be overlooked.
He also has experience in the Premier League, another factor which makes him extremely viable should the Gunners not be able to attract the big name they would prefer.