Having finally sealed the purchase of Adam Lallana, as reported on the official club website, Rodgers has clearly not finished with his summer transfer business as he eyes up the defensive duo, per Paul Joyce in the Express:
Manager Brendan Rodgers wants to continue the reshaping of his squad by bringing in left-back Bertrand with whom he worked when he was youth coach at Chelsea.
Bertrand spent the second half of last season on loan at Aston Villa and is rated at around £7m by the Stamford Bridge club, who had been reluctant to previously deal with a direct rival following the success of Daniel Sturridge's switch to Anfield.
The 24-year-old Bertrand is unlikely to be able to tie down a first-team spot at Chelsea with Cesar Azpilicueta already a regular starter at the club and Atletico Madrid's Filipe Luis reportedly being targeted to replace the departed Ashley Cole, per Alex Harris in the Express.
However, Liverpool are weak in the left-back position and were forced to play Jon Flanagan out of position for the majority of last season.
Thus, despite Chelsea's potential reservations, Bertrand may be eager to force a move through to Anfield in the pursuit of regular first-team football.
Liverpool's much-rumoured pursuit of Sevilla's Alberto Moreno seems to have stalled, and Bertrand would represent a fine alternative, young and talented as he is, but also with some experience at the top level—he has a Champions League winners' medal having debuted in the competition in the 2012 final against Bayern Munich.
Lovren was part of a very strong Southampton side—including Lallana and another Liverpool summer recruit, Rickie Lambert—who finished eighth in the Premier League last season and conceded fewer goals than the second-placed Reds, per ESPN FC.
Tactics expert Michael Cox marks out Lovren as one of the best central defenders from last season's Premier League:
Joyce reports the Croatian international as valued at £15 million and also suggests that the 24-year-old is keen to make the switch to Anfield.
Rodgers desperately needs added strength at the back with the Champions League to contend with next season. The Anfield outfit conceded 50 goals in the Premier League last season, one of the main reasons they fell short of winning it.
Lovren would be a strong addition at centre-back and should be Rodgers' primary concern although Bertrand would, at least, bring a recognised left-back into the squad.