The Merseyside club have opened talks early in an effort to secure a swift deal when business reopens on January 1.
They are prepared to make a formal bid after exploring numerous options to ensure Rodgers is not left without a striker for the second half of the season.
Chelsea are likely to accept an offer as high as £15 million and if they sell Sturridge will seek to replace him with a fresh approach for Bayer Levekusen's Andre Schurrle.
Liverpool tried to sign Sturridge last summer, but that was only on the basis of a season's loan. Up until the final stages of the last transfer window, the club were still in negotiations but Chelsea rejected a temporary proposal. They were only interested in as much as £15m to make the move permanent.
At that time, Rodgers was not entirely convinced he should spend so much on the 23 year-old, who joined Chelsea for just £3.5m.
He was not willing to take a deadline day gamble in August, but the Liverpool manager has reassessed the situation in the last few months.
Sturridge also fits the profile of Liverpool's owners, Fenway Sports Group, who have consistently made known their preference for signing players of international pedigree at a younger age.
One of the concerns Rodgers harboured last August was the former Manchester City striker publicly stated preference to play in a central role. Rodgers will hope to convince him the fluidity of his attacking formation will suit his game.
Since moving to Stamford Bridge in 2009, Sturridge has been unable to make himself a permanent fixture of the starting XI under numerous managers.
After seeming to impress Andre Villas-Boas at the start of last season, he was relegated to the bench again when Roberto Di Matteo took over.
Sturridge has made no secret of his frustrations in west London since then and only last week he made it known how desperate he was to play more regularly - something which eludes him at Chelsea.
"It is difficult to judge me as a player and say my goalscoring record is this or that when I do not play regularly," said Sturridge.
"Not playing regularly is the most difficult thing for anyone to handle."
Sturridge was first considered by Liverpool as a potential recruit two years ago when Fernando Torres moved to Chelsea.
He was mentioned in a possible swap deal in January 2010, but Liverpool decided they wanted a £50m straight cash deal instead.