The Reds are looking to bring in a new left-back as Jose Enrique has been ruled out with a knee injury until February.
Chelsea rejected an move from Liverpool for Bertrand in July, but the 24-year-old has failed to become a regular at Stamford Bridge.
The Daily Telegraph reports that Liverpool boss Brendan Rodgers is ready to make a renewed bid to sign the England international in the January transfer window.
Sunderland and Cardiff are also reportedly interested in the highly-rated defender.
Reports claim Chelsea could demand around £8million for the defender.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.