The 23-year-old is growing increasingly frustrated by his lack of regular first-team action in west London, and is believed to be pushing for a January move.
After Liverpool lost out on top summer target Clint Dempsey - who instead joined Tottenham Hotspur from Fulham - due to the club's hesitation, Brendan Rodgers is keen to swerve a similar farce by reaching agreement for Sturridge now with Chelsea.
The Reds boss is prepared to take a chance on the fringe England international, even though he was reluctant to pay a fee in the summer, and preferred to initially bring him to Anfield on loan.
Sturridge is yet to feature for Chelsea under the interim management of Rafael Benitez due to being sidelined by injury. But, he has been included in the club's forthcoming tour squad that flew to Japan at the weekend ahead of the Club World Cup.
It's not yet clear what Benitez's stance is on Sturridge's long-term future at Stamford Bridge, but the assumption is that his temporary appointment will not impact on the Liverpool deal that was first mooted well before he arrived.