The former Welsh international midfielder, who represented Leicester during his playing days, suggested that the losses of midfielder Esteban Cambiasso and manager Nigel Pearson would be difficult for the side to cope with, and he also expressed doubts over Claudio Ranieri's appointment.
"The jury is out on Claudio Ranieri," Savage said before the season started. "The charming ‘Tinkerman’ hasn’t pulled up any trees lately, and he will struggle to live down being the Greece manager who lost to the Faroe Islands.
"Leicester will miss Esteban Cambiasso – and they will miss Nigel Pearson. Close shave with relegation ahead?"
Leicester have actually already shown that they should easily have enough to avoid any relegation fight this season.
Ranieri has built on what Pearson created at the King Power Stadium towards the back end of last term, and they look a very strong team.
The Foxes have been scintillating going forward, and they already scored 17 goals this term, with Manchester City the only team in the entire division to have a better total.
This attacking class has guided Leicester into fifth position in the table, and although much can happen between now and May, their start should ensure that relegation isn't a concern.