Inter Milan have confirmed their interest in Cardiff's Gary Medel but have given up on Man City forward Stevan Jovetic.
Jeffrey Schlupp and Liam Moore have signed new deals with Premier League newcomers Leicester City.
The 17-year-old winger has been a revelation at Anfield this season and played a key role in the 3-0 win over Wigan at the weekend.
But Sterling, who made his England debut earlier this month, cannot sign a professional contract until he turns 18 next month - potentially opening the door for other clubs to swoop.
Rodgers is unconcerned by that situation because he is confident that the player is enjoying life with the Reds.
"The message is very simple - any club wanting to sign him would be wasting his time," said Rodgers.
"Raheem is in a really 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 himself down to a new contract because he wants to be here and he can be a 'great' at this football club.
"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."