The 31-year old attacking midfielder continues to struggle for regular game time at Anfield and has been linked with another loan spell away from the Reds following his successful stint with Lille last season.
Rodgers is of the belief that Cole is the one who decides his fate whilst playing coy on any potential exit in January.
"I'm just going along game by game," Rodgers told the Liverpool Echo. "There is every opportunity for every player.
"It's not just about the games. Every player gets a chance every single day to show what they are all about.
"Is his future here? You would have to ask him that.
"If he's not going to play as often as he wants then he's no different to any player really. Players are about game time and money.
"But he's not any kind of problem, he's a good guy and we will see what happens over the coming months."