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Liverpool cancelled a meeting with Sterling on Friday because of comments attributed to the player's agent.
Aidy Ward reportedly said the England forward, 20, will not sign a new deal even if offered "£900,000 a week".
Rodgers said: "Raheem has two years left on his deal and I expect him to see that two years through."
Rodgers said Sterling would be available for selection for the team's last game of the Premier League season against Stoke on Sunday and insisted the player would not be unhappy with the prospect of having to stay at the club.
"We want to resolve the situation but it doesn't change my approach to him. There is no problem there," he added.
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"I don't see Raheem being unhappy. Raheem's representative made it very clear that he wanted to speak at the end of the season.
"Our concentration is on the last game of the season and I'm sure talks will take place over the course of the summer."
The England international has already rejected a new £100,000-a-week contract with the club and was expected to tell Rodgers and chief executive Ian Ayre at Friday's cancelled meeting that he wanted to leave this summer.
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Ward told the Evening Standard that he did not care about the PR of the club and used a four-letter expletive to describe former Liverpool defender Jamie Carragher, who has criticised the player.
"He's not signing for £700,000, £800,000, £900,000 a week," said Ward in the newspaper interview.
But Rodgers said the club would attempt to continue with contract discussions "as private as possibly can be".
"Whatever conversation I have with a player or member of staff will remain between us," added the Northern Irishman.
"The owners have shown their strength in their time here. When they have had to show that strength with players they have done that."
Liverpool manager Brendan Rodgers has said he expects forward Raheem Sterling to stay at the club for the remainder of the two years on his contract.