Rodgers said that the 18-year-old should put pen to paper before this weekend's Premier League match with Fulham.
Rodgers said: "Hopefully it will be done in the next 24 hours. There was never any real issue, it was just a matter of time. We were always calm.
"I speak a lot with Raheem and his representatives and there has never been any issues from their side. It was just making sure that we take care in terms of the financial and football plan for the player.
"This was about a young player who has rocketed form playing in the youth teams and the reserves into becoming a full England international, so a lot has happened in his young life and it was just about making sure that there was that protectiion for him going forward.
"I have always been confident that this was going to be the best place for him. The kid is very focused and devoted to Liverpool. His representatives know this is the best place for him.
"Once it gets concluded, he can start to the next part of his development and hopefully he can keep progressing."
Sterling has made a huge impact this season and earned a first call-up to Roy Hodgson's England squad for their World Cup qualifier against Ukraine in September.
He made his first appearance for the senior team in October in England's 4-2 friendly defeat to Sweden.
Sterling, who joined the club from QPR in February 2010, had 18 months to run on his existing deal.
His first-ever Premier League goal came in October when he netted in a 1-0 victory over Rodgers' former club Reading.
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