Sterling's current deal is due to expire at the end of the 2016-17 season, with the player and club widely reported to be in talks over an extension in recent weeks.
And manager Rodgers says he expects the details to be finalised in the near future.
"The club are speaking to Sterling's representatives," he said.
"I would think that would be completed very imminently. The player is very happy."
Daniel Sturridge, who has suffered with a combination of calf and thigh injuries for much of the season, will not be available for Saturday's FA Cup fourth-round tie with Bolton Wanderers, and Rodgers confirmed he will make alterations for the clash at Anfield.
"We'll make some changes," he said. "But we want to win. We'll look at our squad and it's there to make changes, but not too many.
"Jordan Rossiter will be involved. We have some great young players.
"The academy has done a wonderful job aligning players to our philosophy."