The Black Cats are fighting with Newcastle Unied and Norwich City for 17th place.
The Black Cats slid back into the relegation zone on Saturday afternoon as they drew 1-1 with Stoke City, courtesy of a last-gasp penalty from Jermain Defoe.
In contrast, fierce rivals Newcastle were 1-0 winners over Crystal Palace, which helped them move out of the bottom three for the first time since Rafa Benitez took charge.
However with only a point separating each side right now the battle is far from over, and Keown says he believes Sunderland are still favourites to escape.
“Still I think Sunderland look favourite to get out of trouble,” he told BBC Sport. “They’ve got that extra game. If we’re saying that Tottenham will get beat by Chelsea then that’s a Chelsea team that will arrive there with plenty of confidence.
“And then there’s Everton and Watford to follow. They need six points.”
The big problem for Sam Allardyce’s side is that their performances are not getting the results they require at present.
His side have played very well over the last few weeks, but crucially they have not been securing victories, causing the fight for 17th place to go down to the wire.
Crucially though, Newcastle have been picking up wins under Benitez, and that could see the Black Cats go down despite what Keown believes.