The English playmaker has been linked with Newcastle United this summer.
Asked whether there had been dialogue between the two parties, Rodgers said: "I believe so, I believe they've spoken. Yeah, Jon (Rudkin, director of football) has spoken to them a number of times, yes.
"I'm pretty sure the club would want to do that (tie him down). Both sides have to be able to find an agreement.
"With James, with two years left, naturally the club would want to protect the asset. But it works both ways.
"Sometimes, everything goes onto the club. If a player, I'm not saying James, doesn't want to sign it, then it can be a stalemate.
"But absolutely, he's an outstanding player and of course, Leicester City would benefit from keeping him longer."