Rodgers has told England Under-21 winger Gray he has no future at Leicester.
The manager said: "It's pretty clear with Demarai he's looking to move on. His attitude to training has been first class, he has been very professional.
"He is at the stage of his career where he has been here a long time and hasn't maybe nailed down a place. A fresh start may be the course for him.
"I will always respect him and until his last day I will never discard him but it's looking more than likely he will probably be somewhere else next season."