The Daily Star says Drogbaâ€™s management company have rubbished reports he has left Chinese club Shanghai Shenhua.
But his future there seems uncertain amid reports of a power struggle and the clubâ€™s inability to pay his wages.
If he were released the 34-year-old would become a free agent, enabling Rodgers to make his move.
â€śI will have to ask the question, wonâ€™t I?â€ť Rodgers admitted.
â€śAny player I believe can improve the squad, I will look at. There is absolutely no question about that.â€ť