Rodgers says he needs to find a replacement for West Ham United signing Andy Carroll after Friday's deadline day shambles.
Asked about Drogba, who could be available from Shanghai Shenhua, Rodgers replied: "I can't say no. Any player I believe can improve the squad, I will look at.
"We have a very small group. We had 19 training (on Friday). It is something that would have to be discussed."