Gary Neville believes Hull will get relegated but thinks head coach Marco Silva could be destined for a top Premier League job.
Hull's 2-0 home defeat by already relegated Sunderland on Saturday combined with Swansea's 1-0 win over Everton left Silva's side in 18th place, one point from safety with two games remaining.
They travel to Crystal Palace on Nissan Super Sunday, before facing Tottenham on the final day, but Neville says their failure to beat Sunderland could be the "killer blow" to Hull's survival hopes.
When asked to pick between Hull and Swansea to beat the drop, the Monday Night Football analyst said: "Swansea. I think the Everton win was a game-changer.
"I look at the fixtures and Hull are at Crystal Palace, while Swansea are at Sunderland and at home to West Brom. Hull need a huge swing for it to turn again.
"Their failure to beat Sunderland at home could be the killer blow."
Silva and Swansea boss Paul Clement were appointed three days apart in January and each have managed 16 Premier League games.
Hull were bottom at the time with Swansea in 19th, but their form has picked up and each has a chance of securing survival.
Speculation in the English media has linked Silva with several jobs in the Premier League but Neville believes Clement also deserves recognition.
"They have both done brilliant jobs," Neville added.
"I thought both of them were finished around Christmas and I think it's a brilliant achievement to get where they've got to, to be still fighting to stay up. One of them will.
"It's interesting from a perception point of view. Silva seems to be getting the links to the big clubs.
"Clement doesn't, even though he's got that history of being at Real Madrid and Bayern Munich. Obviously he had a tough time at Derby.
"But it seems like Silva's destiny is set in terms of getting a big job in the Premier League.
"I wonder whether that's something Clement deserves as well because they have done similar jobs in terms of what they have achieved."