Swansea host the Tigers live on Sky Sports just three days before their European showdown with St Gallen, with qualification to the next round yet to be secured by Michael Laudrup's side.
The Swans have numerous injury concerns to manage, particularly in the strike-force, and may need to prioritise in certain areas with two matches in swift succession.
However, Davies is under no illusions as to the way Swansea will be leaning, claiming the Premier League holds much greater significance for the Welsh club.
"I would probably say they're not really as interested in the Europa League game as they are in the Premier League," the centre-back said.
"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."
Monday's trip to South Wales will be a return to an old haunt for on-loan Hull striker Danny Graham.
The forward's goal drought - which totals 13 matches for Hull but 30 in all, including the end of his Swansea term and a disappointing spell at Sunderland - is rapidly becoming a concern for the Tigers.
Davies admits Graham is not avoiding good-natured laughter on the training ground but the skipper remains confident in the 28-year-old's abilities.
"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 added.
"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."
Despite not being able to find the back of the net, Davies insists Graham's work ethic remains second-to-none.
"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," he said.
"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."