Hart was also dropped by Pellegrini last November, before eventually winning his place back from Costel Pantilimon.
"If I was Joe Hart and I'm not back in the Man City team soon I'd look to move in January," Savage told BBC Sport. "If you're not playing, you're not first choice for your team, you cannot be first choice for your country.
"It's harsh on Hart, who has played very, very well this season. But if he doesn't play on Tuesday against Roma then it's clear he's not being rested, he's been dropped."
Hart joined City from Shrewsbury Town in 2006.