The 17-year-old has been a revelation this season, breaking into the first team at Anfield and also earning his first England cap, and the Reds are set to move quickly to keep the young starlet on Merseyside.
"The club and his representatives are in good dialogue and good communication, and hopefully we'll get that resolved very soon," Rodgers told reporters.
Sterling has made 21 appearances already this season, and the former Swansea boss has admitted he is slightly concerned about burning the youngster out.
"There will be at some point and we'll need to give him a breather, there is no question [about that]," Rodgers said. "He's a very young man and is still learning the game. He still has technical elements he needs to improve upon and tactical elements.
"But one of the biggest things is psychological at this level - real mental fatigue can set in. He's been terrific so far. He's got to this stage at the end of November and been absolutely brilliant, but at some point he will need that breather. He's been one of our leading players, but for the benefit of Raheem it'll be something I'll need to consider."