Toure joined Celtic on a free transfer last summer, but he only made 13 appearances for the Scottish giants during the 2016-17 campaign, and his contract with the Hoops is due to expire on Friday night.
Rodgers has admitted that it is "a tough one" when considering the future of the experienced defender, although the Celtic manager insists that there will be still a role for the Ivorian if he wants it.
"It's a tough one. Kolo is still in that mindset where he is asking: 'Do I want to play?' He's now 35. "He was fantastic for us last year, but his contract has run out. But he is someone I would like to have a role for," the Evening Times quotes Rodgers as saying.
"Obviously, the playing role diminishes for him. He just needs time to see where he's at, in terms of playing, or whether he falls into the coaching role more.
"It's something that he and I have spoken about over the course of the season. I think that's sometimes what happens is that players who have been at that level, and have that experience, they sometimes just get pushed to the side a little bit. But guys like that are very, very important, not just for changing rooms, but for clubs."
Toure has represented Arsenal, Manchester City and Liverpool during a glittering career, winning two Premier League titles and two FA Cups during his time in English football.