Sterling's future has been the subject of intense media scrutiny since he put contract talks on hold with his agent Aidy Ward saying this week that the 20-year-old would not extend his stay even if he was offered 900,000 pounds a week.
Liverpool scrapped a meeting with Sterling on Friday to discuss his future following Ward's comments but Rodgers expects talks to resume after this weekend's final game of the season at Stoke City.
"The facts are simple. Raheem has two years left on his deal at Liverpool and I expect him to see the two years through and continue to behave as immaculately has he has done since he came to the club," Rodgers told news conference on Friday.
"Raheem has made it clear he wants to speak at the end of the season so for us the concentration is on the last game and I am sure talks will take place over the course of the summer.
"I have not seen Raheem being unhappy. He is a young boy who has developed incredibly well over the last three seasons and I hope the development continues."
Sterling's relationship with Liverpool hit troubled waters in April when he gave an interview to the BBC, saying he was in no rush to sign a new contract but denied being a "money-grabber".
He won the club's young player of the year award on Tuesday and was jeered by some supporters, while others shouted "Stay, Raheem" as he picked up the accolade.
Fifth-placed Liverpool face Stoke City on Sunday and Rodgers said Sterling was available for selection as he remained on good terms with the one of England's brightest young prospects.
"My relationship with Raheem has not been affected," he said. "Raheem has the opportunity to play for one of the greatest clubs in the word and has done exceptionally well.
"He is a good kid, matured very well over last few years and is a wonderful young football player. There is no problem there.
"Liverpool supporters always back their own players. If he plays any part in the game, Raheem will get the support of our fans."
(Reporting By Michael Hann; Editing by John O'Brien)
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