With the Reds’ current backline options far from impressive, defensive reinforcements are seen as a priority for the coming transfer window.
Caulker only joined Cardiff for £8.5m last year, but with the Bluebirds currently staring at an immediate return to the Championship, a quick exit is possible.
Rodgers is said to see the 22-year-old as a possible addition as he plans for the potential exit of Daniel Agger.
Kolo Toure and Martin Skrtel have impressed on occasions, but it is thought that a long-term partner for Mamadou Sakho is on the agenda.
Caulker is known to have a good knowledge of Rodgers’ playing style, and the former Swans coach is confident that he can step up to perform consistently for a big club.
If Liverpool secure Champions League qualification, it is likely that their manager will be backed heavily in the transfer market to make major additions to his squad.
As well as Caulker, Dnipro Dnipropetrovsk winger Yevhan Konoplyanka is a target.