Sterling is under contract until 2017 after signing a new deal worth a reported £30,000 per week but that has not stopped talk of a move away from Anfield.
The 19-year-old is reportedly attracting interest from UEFA Champions League winners Real Madrid, as well as French champions Paris Saint-Germain.
Liverpool are desperate to fend off suitors with a new bumper long-term deal, reward for the England international's rapid rise in the Premier League.
Rodgers is "adamant" Sterling will stick with Liverpool and said: "His agent is a good agent and he understands this is the perfect place for him.
"It's not a big issue for us. [Chief executive] Ian Ayre has spoken with his representatives and he is quite relaxed. The club is dealing with the agent so everything is calm.
"The boy is remarkably happy here and there are no secondary thoughts about anything else other than continuing to play for Liverpool.
"Also, to continue with his development because he still has a lot of growth and for that the best place for him to be is here. His representatives respect that and the club respects that. So that will get sorted out in time."
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