The potential arrival of Davies would push Rose out of his regular place with Tottenham, and the Tigers are ready to swoop to secure a deal to sign the former Leeds United man.
A source told The Mirror: "His future there is looking bleak. At best, he's going to be a bit-part player, and that's not what Danny wants at this stage of his career. He needs to be with a club who can give him regular first-team football.
"Danny's progress has been affected by loan moves and a number of niggling injuries, and now Pochettino has come in and highlighted the left-back position as one that needs to be urgently addressed.
"A move back to his native Yorkshire could be just the job for Danny - and it would be a perfect fit for Hull."
The 24-year-old made 30 appearances in all competitions for Spurs last season.