The BBC pundit feels both will be 'absolutely fine' but for different reasons.
The former Leicester City midfielder had backed the current three sides in the relegation zone to go down and believes Villa and the Magpies will stay up.
For Aston Villa, the Welshman is worried that relegation would dampen their FA Cup final experience, although he feels that is an unlikely outcome.
Indeed, the BBC pundit says Aston Villa will be 'absolutely fine' thanks to the goals of Christian Benteke - the form striker of the top flight.
Savage said: "My worry for Villa was that they would get relegated the week before the FA Cup final, which would make that day a bit of a non-event.
"But Christian Benteke is scoring again and they will be absolutely fine. Their next problem is keeping hold of the Belgian striker, because he is good enough to be playing for a top-four team."
And the Welshman also predicted Newcastle to stay up, despite John Carver's men having lost their last seven games in a row.
Savage backed the Magpies but, interestingly, thinks the only side capable of dragging them into the mire are Tyne-Wear rivals Sunderland.
The Black Cats have difficult fixtures, however, and the BBC pundit feels that will favour Newcastle.
He said: "Sunderland are on 30 points and have a game in hand, so are looking at two wins out of five to go above their north-east rivals - but in effect it is two wins from three because their final games are away at Arsenal and Chelsea and I cannot see them getting anything out of either.
"The Black Cats managed it last year - it looks like Newcastle are safe unless they do it again."
Newcastle travel to Savage's old side Leicester for Saturday's early kick-off, while Tim Sherwood's Aston Villa host Everton at 3pm.