The BBC pundit thinks the Black Cats are doomed this season.
Sunderland find themselves third from bottom and therefore in danger of relegation from the Premier League should things not improve for them with five games to go.
And Savage feels the writing is on the wall for the Wearside outfit, suggesting their 'gamble' of replacing Gus Poyet with Advocaat has failed to pay off as Sunderland's defence is still 'shocking.'
The former Premier League midfielder said of the Black Cats: "[Sunderland are] Going down. There will be no Great Escape this time.
"It was a gamble to change their manager when they did and bring in Dick Advocaat with 10 games remaining.
"He had an initial impact with a win against Newcastle but, defensively, the Black Cats still look shocking. That is the main reason they have won just one of their last 10 games."
Intriguingly, as the formbooks show, four Premier League teams have performed worse than Sunderland since Advocaat took over at the Stadium of Light.
But it is the fact that this most recent form is allayed with a poor campaign under Poyet, as well, that leaves the Black Cats in the bottom three.
Sunderland have Arsenal and Chelsea still to face this term, as well as three other grueling fixtures. Can they prove Savage wrong?
Advocaat's men host Southampton on Wearside on Saturday afternoon at 3pm.