Steve Bruce maintains 10 victories would be enough to keep his side in the Premier League and need just one more to reach that milestone ahead of next week's FA Cup semi-final
Bruce set his sights on 10 wins at the start of the season to stay in the Premier League, and victory this weekend would see that milestone passed before Hull switch their attention to matters elsewhere.
Hull will visit Wembley for the second time in their history to take on Sheffield United in next week's FA Cup semi-finals, having reached the competition's final four for the first time since 1930.
However, a recent downturn in form has sharpened the need for Bruce's side to forget their cup run and secure safety in good time.
The sides go into Saturday's meeting locked on 33 points, with Swansea a place above Hull in 13th by virtue of goal difference.
Strength at home has been key to Hull's impressive return to the top flight, but victory over West Brom at the KC Stadium two weeks ago was their first in the league since the turn of the year on their own patch.
Swansea themselves are on a wretched run away from the Liberty Stadium, having picked up just four points from the last 30 available on the road.
Coach Garry Monk claimed ahead of the game he is targeting wins from each of Swansea's remaining six games, although he concedes his side must be at their best to begin that sequence in Yorkshire this weekend.
"It will be tough," he said. "But I also think it will be a good game.
"People will talk about their recent results, but overall they have had a good season. Many people wrote Hull off before the season started and they have proved them wrong so far.
"They have good, experienced players and we'll need to match their intensity and will to win the game."
Monk has a full first-team squad to choose from for the game, while Bruce will welcome George Boyd back to the fold following his three-game ban for spitting at Manchester City goalkeeper Joe Hart.
Bruce admitted Boyd was set for a run in his starting XI before his suspension, and the Scotland international could be due for a return to the side with Sone Aluko failing to find form in his place.
Yannick Sagbo's inclusion is up in the air after he was hit with a Football Association charge in the week for postings on social media concerning the controversial 'quenelle' gesture.