The BBC pundit feels the 34-year-old should be used differently by the Reds.
The former Premier League midfielder feels the time is right for the Liverpool captain to leave Anfield at the end of the current campaign, with reports last night suggesting that will indeed be the case on Merseyside.
But Savage feels Gerrard should be played in defence - not midfield - until he leaves.
"I think he’s been Liverpool’s best ever midfield player but I think the time’s right [for him to leave at the end of the season]," Savage said of the skipper on Match of the Day.
"If you are going to play him for the rest of the season, I’d play him in the back three."
Former Arsenal defender Martin Keown, however, disagrees that the time is right for Gerrard to leave Liverpool.
"I don’t agree, I think you should keep your best players as long as you can. It must be Gerrard’s decision and you can’t blame him for where Liverpool are in the table," Keown explained.