The Scotland international has long been linked with a move away from Liverpool and the likes of Everton and Fulham are reportedly interested in signing the midfielder.
"Charlie was brought in for a lot of money after a terrific time at Blackpool," said Rodgers.
"Last season was a wee bit broken in terms of injury but he has trained well in pre-season and will play against Hearts.
"He's a talent - everyone knows that - and he played well in the last Scotland game.
"You never forecast anyone's career and all I can talk about is the here and now. At the minute he's working hard and looking to fight for a place.
"I actually tried to buy Charlie when I was manager of Reading so where these stories come from, I don't know."