Reports have suggested that the 19-year-old has caught the eye of the Spanish giants after his impressive performances for both club and country, but Rodgers says the winger is happy at Anfield.
"You could link Raheem with every club in the world at the moment," Rodgers told reporters ahead of Liverpool's clash against neighbours Everton on Saturday. "I sit easy with it."
"I've nothing really to add to it. There's obviously lots of speculation every day about players coming and going here at Liverpool.
"He's a wonderful boy who's developing very, very well here. I think him and his representatives and the people close to him know how comfortable he is here and I'm sure at some point in the future, whatever contract we're looking to work with will be sorted, but he's still got three years left and there's no rush from my perspective."
Sterling played all 120 minutes of the Reds gruelling League Cup victory against Middlesbrough on Tuesday night, which they eventually won 14-13 on penalties. Rodgers says that playing again so soon won't be an issue for the England international, who was one of the three players to miss from the spot in the historic shoot-out.
"Raheem is a super fit boy," Rodgers added. "Playing 120 minutes in midweek won't be a problem for him."
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