The Welsh striker, who has been selected in the Team GB Olympic squad, has been linked with a return to Cardiff City but former Swansea City boss Rodgers will continue to hold talks with the veteran to try and keep him at Anfield.
"I had a good meeting with Craig, last Monday and was just getting the feel for where he was at," he said.
"I've known Craig for a little while and we had a good open conversation.
"He's 33 later this week and so he knows he's pushing on in age a little bit, but he's fine. He looks after himself well.
"I'll speak with him over the course of the summer and we'll take it from there."