Sterling has enjoyed a meteoric rise to prominence over the past 18 months and is now a key figure for Liverpool and England after a series of impressive displays.
Recent reports suggest Carlo Ancelotti has placed the 19-year-old top of his wanted list as Real Madrid look to continue their policy of acquiring the most exciting attacking talent in European football.
Rodgers admits Sterling's recent form makes speculation inevitable but insists he is not worried by talk of a transfer.
"You could link Raheem with every club in the world at the moment," Rodgers told reporters. "I sit easy with it."
Sterling played 120 minutes as Liverpool were forced into the longest penalty shootout in League Cup history on Tuesday, but Rodgers insists he has no concerns about including him in Saturday's Merseyside derby clash with Everton.
"Raheem is a super fit boy," he added. "Playing 120 minutes in midweek won't be a problem for him."
Liverpool have endured a difficult start to the season as they continue to adjust to life without Luis Suarez and Rodgers admits it will take time for his team to regain its attacking rhythm.
"When you lose a core of players it becomes a bit broken," he continued. "That's how our game has been."