That’s according to national reports in The Mirror, who claim the highly-rated 20-year-old is on Blues boss Kenny Jackett’s radar.
However, the same story claims that Stoke are also interested in the full-back.
The Mirror also say that Leeds manager Marcelo Bielsa’s would prefer Davis to join the Potters if a move is sanctioned.
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Pompey currently have Lee Brown as their only senior option at left-back, after he signed a new deal with the club earlier this month.
They want further reinforcements in that position, though, and are actively looking to bolster their numbers in that department.
Brighton youngster Alex Cochrane is high up that list, but The News understands that the Seagulls are reluctant to allow their academy product to move where there’s no guarantee of regular minutes.
Leeds youth product Davis has made 10 appearances for the Elland Road outfit, with five of those appearances coming last season.
He currently finds himself well down the pecking order at the recently-crowned Championship winners, with Stuart Dallas, Barry Douglas and Ezgjan Alioski all ahead of him.
However, Bielsa is keen to get him out on loan to build up his match-day experience.
Last year, the highly-rated Whites full-back was linked with moves to Liverpool and Bournemouth.