Sterling, 20, who has made 112 appearances for the club, is now a regular starter with nine goals in 33 appearances this season, but there has been considerable speculation he is being courted by Real Madrid and Barcelona.
"He has been offered a wonderful deal, an incredible deal for a young player of 20 who is still developing," Rodgers told reporters on Monday ahead of the Premier League game against Tottenham Hotspur on Tuesday.
"He has made some great strides in the last couple of years and he should now get the reward for that and I hope his representatives can find agreement with the club.
"I know the player is very happy and wants to continue working the way he has been. I have spoken to him a number of times -- he is happy here and you can see that in his game.
"It is not just a case of giving any player what they want. I am saying we want to reward our best talents -- they are a big part of our future and I am confident that will all be agreed very soon."
Rodgers also hopes that 19-year-old winger Jordon Ibe, who made his first Premier League start for Liverpool in the goalless Merseyside derby against Everton on Saturday, will sign a new deal at Anfield.
Liverpool start the match four points and two places behind a Spurs side who are on a high after their pulsating 2-1 win over Arsenal in the north London derby.
Liverpool are likely to be without Brazilian midfielder Lucas Leiva who faces a scan on an abductor muscle injury he picked up against Everton.
However, Adam Lallana should be fit after missing the derby with a groin injury, while Philippe Coutinho (knee) and Sterling (foot) are expected to feature despite taking knocks at Goodison.
Tottenham will be hoping to improve on a poor recent record against Liverpool having lost their last four matches against them, with the last three ending in 5-0, 4-0 and 3-0 wins for Rodgers's side.
(Reporting by Mike Collett; editing by Michael Hann)
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