The highly rated forward is set for Anfield medical after the two clubs agreed a £12 million fee, with the player given a £60,000 per week contract.
According to the same source, it is highly unlikely that the transfer will be officially announced before the start of the January transfer window.
Liverpool have been desperate to sign a new striker to help Luis Suarez up front and the arrival of the England international should be a huge boost for the club.
Sturridge has so far failed to prove his worth at Stamford Bridge, partly due to the fact he was constantly being played out of position.
The move to Liverpool will not only give the player a chance to kick-start his career, but will probably see him finally deployed as a centre forward.