The move will leave Rafael Benitez, who is keen to provide Fernando Torres with more support, with just one recognised centre-forward.
The interim manager confirmed last night he will discuss transfer targets with the club's hierarchy later this week and a move for Atletico Madrid's coveted goalscorer Radamel Falcao is highly likely.
Benitez has not used Sturridge once since his arrival. At his press conference yesterday, the Spaniard admitted there were "conversations with different options" for Sturridge's future. The player's chosen destination is Anfield.
Brendan Rodgers, the Liverpool manager, is keen to add to his flimsy striking resources.
Summer signing Fabio Borini broke his foot in October and the responsibility given to Raheem Sterling (18) has been greater than Rodgers had hoped through necessity – he has already started 17 games.
Rodgers also hopes to sign Blackpool's 20-year-old winger Tom Ince in January, 16 months after Liverpool sold him to the Championship club.
If Sturridge goes, the pressure will increase on Chelsea to buy new strikers. They are almost as limited in their options as Liverpool, with only one fit senior forward, Torres, who is nowhere near the form of Suarez.
"We have time before January," Benitez said when asked when he would be planning the club's strategy for new signings.
"We have just arrived home (from Japan) and then (we have) another game.
"Hopefully, we have two or three days after this game, and then we have plenty of time.
"We are still working, the people in charge are working, and we will talk about names."
Benitez's chief ally will be Michael Emenalo, the technical director. "We can chat every day," said Benitez.
"So, Michael is watching the training sessions and we talk about players, the team and what we need. I know what he likes, he knows what I like. It is just about agreeing."
Chelsea may well pursue Falcao, the third top-scorer in La Liga with 14 goals already this season.
Another issue on Benitez's agenda is club confidentiality.
Chelsea are set to remind staff to be more careful with their documentation after two sheets of paper detailing tactical plans for corners were found in the dressing room of the Nissan Stadium in Yokohama following Chelsea's 1-0 defeat to Corinthians in the Club World Cup on Sunday.
Oscar, the Brazilian midfielder, was upset not to have played against Corinthians, but Benitez insisted there are no problems with the 20-year-old.
"Oscar is a very good lad, a very good professional," he said. "His reaction has been very positive. We don't have an issue here."
Benitez also explained that he needs to start rotating the squad to cope with the demands of a congested fixture list.
"The problem we had was Chelsea were playing with (the same) 11 players the majority of the games," he said.
"We have to change this. Because you cannot carry on – especially now at Christmas time, with a busy schedule – playing the same players all of the time." (© Independent News Service)