The 17-year-old has been expected to sign a long-term deal at Anfield after a fine start to the season, but is unable to sign his second professional contract until he turns 18 in December, prompting suggestions that he could leave in search of higher wages.
The Reds manager, however, is sure that the winger's future lies on Merseyside and hopes that Sterling, along with the club's other young players, can lead the club to glory in the coming years.
He told The Sun: "The message is very simple – any club wanting to sign him would be wasting his time.
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"Raheem is in a real good place here. He has been given an opportunity here this season and he is thriving on it and enjoying the work. He will tie down himself to a new contract because he wants to be here and he can be a great here at this football club.
"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 stars.
"We want him to continue to grow, and why would you want to leave one of the biggest clubs in world football? So it’s a no brainer."
The Northern Irish manager went on to hail Sterling's performance on Saturday in which he set up the Reds’ first two goals in 3-0 home win over Wigan, just three days after he made his England debut in a friendly against Sweden.
"Raheem is just amazing," Rodgers beamed. "He came off the back of playing 86 minutes for his country, and looked like he could play another 90 minutes at the end of this game - the club has got a fantastic talent.
"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, you see him and Suarez combining better in each game and that is a tribute to them and how hard they are working on the training ground.
"I think what we are seeing now the players understanding the method of the team more. Raheem is getting that, and his contribution in making two goals showed it."