Cole scored his first Barclays Premier League goal since April 2011 in Sunday's 3-2 win at his old club West Ham but the 31-year-old midfielder has been out of action due to injury for bits of the season, and when fit for selection this term has only started cup matches.
And reports have suggested he could be set for a move while on that matter, Rodgers will "see what happens", saying on the Liverpool Echo website: "I'm just going along game by game. There is every opportunity for every player."
Rodgers added: "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.
"The guy is still a Liverpool player and while he's a Liverpool player I'll work as hard as I can with my staff to try to make him the best we possibly can.
"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."