Blues boss Carlo Ancelotti insisted he would use more of his younger players at the start of the season.
But Sturridge was also offered to Liverpool as part of a deal to sign Reds striker Fernando Torres.
Liverpool want ?50m for the Spanish forward and rejected Chelsea's first offer of ?35m.
They also turned down Chelsea's offer of cash plus Sturridge to try and sanction a deal but that was also rejected by Liverpool.
Good signing if it goes through, will put pressure on Davies and Elmander to keep their
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The Reds are said to be open-minded on an arrangement that would include former Bolton striker Nicolas Anelka moving back to Anfield.
Since moving from Manchester City in 2009, Sturridge has struggled to make his mark in a Chelsea side that includes forwards Anelka, Didier Drogba, Florent Malouda and Solomon Kalou.
He has scored nine goals in the two seasons he has been at the west London club. He also has 10 caps for the England under-21 team.
Source: BBC Sport