British media reported on Sunday that Liverpool had reached an agreement with Manchester City to transfer Sterling in a deal worth 49 million pounds.
It would make Sterling the most expensive English player ever, surpassing the 35 million pounds Liverpool paid Newcastle United for striker Andy Carroll in 2011.
Rodgers, speaking at a news conference in Thailand where Liverpool are kicking off their pre-season tour of Asia and Australia, did not provide any specific details on the winger's transfer but confirmed that an agreement had been reached.
"The situation is very simple. The club has agreed with another for a deal for Raheem to be transferred and subject to medical that will go through," Rodgers said.
"Contrary to the last week or so, in terms of what was written, Raheem and I have always remained very strong in our relationship, and have been up until he left. There's no issue there."
City had two bids for Sterling rejected last month after he turned down a pay increase to stay at Liverpool.
The 20-year-old did not fly out with Liverpool for their pre-season tour despite being named in the squad.
Sterling signed for Liverpool as a 15-year-old from Queens Park Rangers in February 2010 and has made 129 appearances for the Anfield club, scoring 23 goals.
But his relationship with Liverpool hit troubled waters in April when he denied being a "money-grabber" in an interview with the BBC, claiming he was motivated purely by ambition.
Sterling's agent Aidy Ward also angered the club and its supporters in May by saying the England winger would not sign a new deal at Anfield -- even for 900,000 pounds a week.
Rodgers, whose side finished sixth in the Premier League last season, was coy about the details, saying he was focussing on the players on the tour.
"I spoke to Raheem at length yesterday, there is no issue. Two clubs have greed a deal and subject to a medical he will move on," the Northern Irishman said.
"It's important for us to improve and build the squad for this season coming. We are pleased with the players we have brought in.
"It's the overall team that is important. We aim to be stronger than last season that will be reliant on everyone."
(Writing by Julian Linden; additional reporting by Michael Hann; Editing by Sudipto Ganguly/Amlan Chakraborty)
