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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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