The Daily Star says Drogba’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 club’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.
“I will have to ask the question, won’t I?” Rodgers admitted.
“Any player I believe can improve the squad, I will look at. There is absolutely no question about that.”