Bruce, 60, has been under a significant amount of pressure by the Magpies fanbase this campaign with strong calls for him to be sacked first emerging in January.
A run of 11 games without a win between December and the turn of the year, which soon extended to two wins in 21, saw United crash out of both cup competitions and plummet towards the relegation places.
Fan anger peaked when Newcastle lost 3-0 at Brighton and Hove Albion last month, however Mike Ashley has been somewhat rewarded for his loyalty to Bruce following back-to-back wins against Burnley and West Ham, plus a 2-2 draw with Tottenham.
The surprise upturn in form has steered the club to eight points above the drop zone, meaning top-flight safety is within touching distance.
However, Savage, a player Bruce managed at Birmingham City, believes there is no going back for the former Manchester United defender in the eyes of the supporters.
Savage, penning his column for the Daily Mirror, insists the atmosphere has become too toxic, which is why he has suggested Bruce departs this summer.
He said: “Steve Bruce is a good man, a good manager, and I believe he will keep Newcastle United in the Premier League.
“But one way or another, I fear his days at St James' Park are numbered and it might be best for all concerned if they part company this summer - because the atmosphere around the club has become too toxic.
“If he stays in place into next season, the fixture computer hands Newcastle a tough start and the fans, readmitted to that fantastic stadium like a fortress overlooking the city, vent their feelings, the environment could be intolerable.
“Let's get it straight: Even if his team's football this season has often been grinding and stodgy, Bruce has not deserved the tsunami of abuse he's copped on social media.
“He loves Newcastle United, he cares about the club and he is a human being.”