The 19-year-old has been cited by the Reds as the back-up for primary left-back Andrew Robertson.
Davis has already made five appearances this season before being hindered by a knee injury.
The Morecambe youth produce is tied with the Elland Road club until 2021 and manager Marcelo Bielsa turns out to be a big fan of the teenager.
The Argentine manager has been impressed with Davis’ progress in the reserves, which led him to his first-team call-up.
Now, the Reds want the Whites left-back as they look to offload the pressure of Scots man Robertson.
Given that the Whites will play in the Championship next season, the Merseyside club can easily lure Davis to the Premier League.
Meanwhile, Leeds will miss one of their promising stars should the English prospect opt for an exit.
Bielsa, who has earned a name for nurturing the young talents seems to have real plans in his mind for Davis next season.
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The Elland Road club was in pole position to secure automatic promotion before derailed in the crucial phase. They also got their second chance in the playoffs only to be defeated by Derby County in the semi-finals.
The Argentine manager expressed his desire to continue at Elland Road, despite his future still remaining uncertain.