The Wales international defender is struggling to force his way into the Spurs side as he sits behind Danny Rose in the pecking order at White Hart Lane.
As long as Rose is fit and well, Davies' first-team prospects are unlikely to improve, and it has been suggested he would jump at the chance to move away.
Conte could be ready to make a move as he looks to bolster his defence in the transfer window, but Davies would also face a tough battle to force his way into the Blues side.
A loan switch to Crystal Palace may be a better option, as reports claim new Eagles boss Sam Allardyce is also lining up a potential swoop for the former Swansea man.
Spurs boss Mauricio Pochettino could also block any move as he will be reluctant to let a key squad player move on without replacing him first.