Caulker played under Rodgers during a season-long loan spell at Swansea City during the club's first year back in the top flight, and The People now claims that the Northern Irishman is keen to reunite with the England international.
It is thought that a central defender will be a priority this summer as Liverpool return to Champions League football and the club may even look to recruit another centre-back with experience of Europe's biggest club competition.
Tottenham Hotspur are believed to have first option on re-signing Caulker as part of the deal that took the player to Cardiff.
However, with Tim Sherwood's future at White Hart Lane reportedly in doubt and chairman Daniel Levy rumoured to have reservations about the 22-year-old's ability, a move to Anfield appears to be more likely.
Liverpool may also be forced to fork out heavily for Caulker, with Spurs set to recoup 50% of any fee for the defender.