Sunderland are currently in 18th place in the Premier League table - and they are one point adrift of safety.
As things stand, Newcastle United occupy the last spot above the drop zone, but Carragher insists that Sunderland’s advantage of having a game in hand over their North East rivals is a major advantage.
“I still would side with Sunderland, just. I think if Sunderland get five points it will be enough. Newcastle will beat Villa, I think it’s a big ask to beat Tottenham," the former Liverpool defender said.
“I think that vital point at Stoke made a difference. Two draws and a win will be enough for Sunderland, I think.”
With Aston Villa already doomed, Norwich City are the other contenders to make it out of trouble.
Norwich have been tipped to go down for some time, but they are still within one victory of safety.
The Canaries, like Sunderland, have also played one game less than Newcastle, but Parker doesn’t feel that they will make it out of trouble.
“If I’m being honest I think Norwich are in a bit of bother, Sam Allardyce is a man who knows what this is about, he’s got teams out of bother before,” Parker added.
“It’s in Sunderland’s hands. If there’s one team you want to be it’s Sunderland because it’s in your hands.
“I still think I’d want to be Sunderland (even though Newcastle have Villa on Saturday). I can see Sunderland picking up some results, to be fair.”
Newcastle’s final two matches come against Aston Villa and Tottenham Hotspur.
Sunderland still have games against Chelsea, Everton and Watford left to play.
Norwich’s final three matches come against Manchester United, Watford and Everton.