Leicester rejected Manchester City's last-minute £60m bid for Mahrez on transfer deadline day.
"Do they have much to gain from keeping a disaffected player at the club? Not in my opinion," Savage wrote in the Mirror.
“No disrespect to Leicester, who are perfectly entitled to hold Mahrez to his contract, but he has outgrown them.
“Are they ever going to offer him Champions League football again? Probably not.
“He's seen other star players being allowed to fly the nest for good money – so why are Leicester demanding a king's ransom for Mahrez?
“A move to City would almost guarantee him winning more trophies, possibly including the Champions League, and a chance to play for Pep Guardiola, arguably the best coach on the planet.
“After everything he has done for Leicester – a £460,000 snip who is now worth more than 100 times as much – surely there comes a point where it is churlish to stand in the way of his ambition."