The 35-year-old Ivory Coast legend is out of contract this summer and was expected to end his brief stay in Glasgow after one campaign.
However, Rodgers is delighted with the leadership and influence the former Arsenal, Liverpool and Manchester City defender has brought to the club and will now discuss the possibility of a backroom role.
The Hoops boss said: “It’s something we’ll talk about at some stage between now and the end of the season, there’s no doubt about that.
“There are other reasons why I brought him here, like that influence in the changing room. And that doesn’t have to end after this season.
“He’s a good guy and I like to help good people. I want to work with him and it’ s something he and I will talk about between now and the end of the season.’
Toure hasn’t played for the first team since the 4-3 win over Motherwell the start of last month with the defensive pairing of Erik Sviatchenko and Jozo Simunovic the preferred option.
The Irishman added: “He certainly loves it. His family have all moved up and they’ve all settled in well. You don’t make that commitment if you don’t think it’s going to be for longer than what his contract was.
‘He knows he’s at a big club in Celtic. It’s only when you come into it that you realise just how big it is.
“Of course, he’ll enjoy like the rest of us the pressure and the expectancy around Celtic to win.
‘When you’ve worked at a big level, that’s what you want and he has that at Celtic.”
“He sees himself going down that route.”