The 17-year-old has scored once in 11 Premier League appearances for the Reds this term after making his first-team debut in a 2-1 loss to Wigan Athletic in March.
The former Queens Park Rangers youth player was handed his first England cap in last week’s 4-2 loss to Sweden, and Rodgers expects Sterling to commit his future to the Reds.
“Raheem is in a real good place here,” said Rodgers.
“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.
“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.”
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news