The Swans have a number of injury problems to manage, particularly up front, and may need to prioritise in certain areas with two matches in swift succession.
And Davies is certain which way Laudrup will be leaning.
"I would probably say they're not really as interested in the Europa League game as they are in the Premier League," said the central defender.
"As much as I think if they get it right Swansea have a chance of winning the Europa League, especially with the way they play their football, their main concern is probably to get through our game.
"Whoever is fit or whoever is not they will be patching them up and then look at the European game.
"The Premier League is the bread and butter for them and they will want to impress here as well as the Europa League."
The trip to the Liberty Stadium represents a return to familiar surroundings for on-loan Tigers striker Danny Graham.
His goal drought - which totals 13 matches for Hull but 30 in all, including the end of his Swansea stint and a disappointing time at Sunderland - is fast becoming a concern.
Davies admits he has not escaped some good-natured ribbing from team-mates on the subject but remains a firm fan of the 28-year-old's all-round contribution.
"We still give Danny a bit a of stick, a bit of banter, and I think he'd feel uncomfortable if we weren't doing that," he said.
"At the same time when we need to gee him up we do.
"The work he does for us as a team is great, he just needs one to deflect off him and go in the back of the net.
"Maybe the goals aren't coming because he's working too hard for us and he finds himself in positions where he's retreated to help the midfield, not in positions in the box where he can nick the tap-in.
"That's credit to him because he's rolled his sleeves up but I'm sure he'd like a goal too.
"It would be brilliant for Danny to nick one at Swansea. He's well-liked there and had a very good time there."
If Graham's barren streak does persist, Bruce is close to giving Matty Fryatt his chance in the Premier League.
Fryatt managed only five appearances last season due to an Achilles injury and was sent on loan to Sheffield Wednesday early in the current campaign.
But he is back now and eager to push his claims.
Bruce said: "I've never really seen Matty play because he missed a year with his Achilles, but thankfully going to Sheffield has done him a bit of good and he's come back into the fold."
- Sports & Recreation
- Premier League
- Michael Laudrup