The 23-year-old England frontman has been heavily linked with a move to Merseyside after slipping down the pecking order at Stamford Bridge.
Liverpool are desperate to bolster their forward line, with Luis Suarez their only fit out-and-out striker and boss Brendan Rodgers has been keeping tabs on Sturridge since the summer.
The Reds have not yet made any comment on the proposed deal but it has been reported that a fee of around £12m will be paid by the Anfield club.
Liverpool cannot officially register any new signing until 2 January when the transfer window opens.
Sturridge has made 14 appearances for Chelsea this season, but only half of those have been in the Premier League, scoring twice - one in the league and one in the Capital One Cup.
He has also broken into the England squad, coming on as a substitute in the recent 4-2 friendly defeat in Sweden, and played for Great Britain at the Olympics.
Chelsea manager Rafael Benitez does not believe the deal has yet gone through though, but admitted it was only a matter of time.
"I cannot confirm but I think so (it will go through)," he said. "There is still no news if we know more I'll let you know."