The former Foxes man believes the win at Manchester City proves the shock league leaders' title credentials and sees no reason why Jamie Vardy or Riyad Mahrez should leave
The Foxes are five points clear at the top of the table with 13 games to play, though some pundits still doubt whether Claudio Ranieri's men can pull off what would be one of the most remarkable achievements in English football history due to their rivals' supposedly greater strength in depth.
However, after watching Leicester dismantle previous title favourites Manchester City 3-1 at the Etihad Stadium, Savage believes the impossible is now possible for a side that was rock bottom of the table at the same stage last season.
Savage, who won the League Cup during his five-year spell with the Foxes between 1997 and 2002, believes Vardy and Mahrez are an attacking duo capable of propelling Leicester to a first ever top-flight title.
"I honestly believe that after that performance against Man City - to go to the Etihad and play like that - that they can go on now to lift the title," Savage told Goal.
"Vardy was playing non-league football a few years ago and now he has just signed a new contract.
"Mahrez was signed for £400,000. It is important they keep hold of him now because the way these two have played together is unbelievable. It's like a film story."
The pair's sensational form has seen them linked with some of Europe's biggest clubs but Savage feels both players can realise their dreams at the King Power Stadium with Champions League qualification a certainty.
"If they do move to a new club, I don't think there will be much of a problem for them because they will still scare defenders with their pace," Savage said.
"Pace is the most valuable thing for them and if Leicester don't win the league and they move to a bigger club, then I doubt they will have problems in adapting.
"But I firmly believe they will finish in the top four, so why leave? Besides, with the increase in TV revenue, Leicester have the money to keep these players."
The decision to hire former Chelsea boss Ranieri was considered a major error in judgement by some, including Savage, with the veteran Italian coach's reputation having been at an all-time low following a disastrous stint in charge of the Greek national team.
However, Ranieri has well and truly won over his critics, both with the remarkable results he has overseen on the field and his endearing conduct off it.
"Before the start of the season I was among those who were sceptical of his appointment but he has proved most of the pundits wrong," the 41-year-old confessed.
"He comes across as a humble, likeable guy. That Leicester team I played with had big characters and was a great team but I believe this team now has surpassed that and I honestly didn't believe they could.
"We finished seventh on two occasions and won two trophies. We had great team spirit, and went to Wembley as well, but this team has grabbed the people's hearts. It's been incredible."