The 18-year old winger has agreed a five-year deal with the Reds which his boss expects him to sign before visit of Fulham.
"Hopefully that will be concluded within the next 24 hours," said Rodgers.
"I have said before that there was never a real issue, it was just a matter of timing and we hope that over the next couple of days that can be complete.
"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."
It is believed Sterling's new long-term contract will earn him around £30,000-a-week to begin with.