Gray, 24, was consigned largely to a role as a substitute last season and is yet to offer any indication he will sign a new deal before his contract expires next summer.
Foxes boss Rodgers said: “It'll be up to him. He's in his last year and he hasn't signed another deal but, for me, I will always respect Demarai and what his wishes are.
“He is working very hard to play a part while he's here. We'll see how it evolves over the course of the season.
“He is now 24 and it'll be whether he wants to continue in the role he's played here or whether he sees himself going out and becoming a starter."