Rafael Benitez is now in charge at Stamford Bridge of course, replacing Roberto Di Matteo – who was sacked last week.
Benitez may see the young England striker as a big part of his plans in the English Premier League this campaign, but the Reds hope that he is willing to let him go in the New Year, like Di Matteo apparently was.
Brendan Rodgers needs strikers and someone like Sturridge could be the perfect buy for him as he is eager to impress and capable of scoring goals at the highest level.
The Merseyside club may even try and land the England international on a loan deal until the end of the season and then make a move permanent in the summer, should he impress at Anfield.
With talks reportedly already starting between the two clubs, it may be too late for Benitez to have much of a say on the future of Sturridge, even if he does want to keep him at the club.
The striker himself is currently out of the Chelsea side with injury, but will be looking to make his way back into the eleven when he returns.