The 17-year-old won his first England cap last week before starring in Saturday’s 3-0 win over Wigan — the side against whom he earned his debut just eight months ago.
Rodgers believes the youngster could become a Liverpool great over the coming years.
“Raheem is in a real good place here,” said the boss.
“He has been given an opportunity here this season and he is thriving on it and enjoying the work. He will tie himself to a new contract because he wants to be here and he can be a great here at this football club.
“The message is very simple: we are trying to move the club forward over the next couple of years and there will be a little bit of pain along the way but there are not too many teams in the Premier League who are starting with three teenagers and he is one of our outstanding players.
“We want him to continue to grow, and others. And why would you want to leave one of the biggest clubs in world football? So it’s a no brainer.”
Sterling claimed two assists as Liverpool extended its unbeaten run in the Premier League to seven games.
“Coming off the back of his international debut and playing 86 minutes as well and then coming back here and playing 90 minutes and looking like he could play another 90 minutes at the end of the game … It’s just amazing,” Rodgers added.
“He is so bright and so sharp and what I like now is that you are seeing that little bit of arrogance with the ball. He is comfortable now. He knows he has a lot to learn and a lot to improve on, but you see him and Luis Suarez combining better in each game and that is a tribute to them and how hard they are working on the training ground.
“He assisted two goals today — the pull-back for Luis which was deadweight and it was his shot that got parried for Jose Enrique to score.
“If you play as a front player your job is simple: it is either to score goals or create goals and then you function defensively.
“The kid has been brilliant. We just have to nurture that.
“I think what we are seeing now is more bodies arriving in the box and the players understanding the method of the team more. We had a lot of bodies in the box today.”