The 34-year-old is planning to train with the Blues in order to keep his fitness up for the Africa Cup of Nations competition in the new year, but his agent Tcherno Seydi has hinted that he could do more than just practice.
Drogba joined Shanghai Shenhua in the summer after eight years at Stamford Bridge, but his season in China has recently come to an end and a loan move to keep him in shape for Ivory Coast has been mooted.
Seydi claims he will be speaking to FIFA to ask for special dispensation to allow the striker to make a temporary switch outside of the transfer window.
Blues boss Roberto Di Matteo will certainly be interested in knowing the outcome of that conversation, particularly in light of his comments after the West Brom defeat about his strikers needing to contribute more.
A potential playing return for Drogba would help see Di Matteo through to the new year, when a bid for Atletico Madrid hitman Radamel Falcao is likely to be made, although he would face competition for the experienced forward, if he becomes available, from the likes of Juventus.
Drogba's representative told L'Equipe: "It would be an exceptional measure, but considering what he has brought to African football we can ask for it.
"Considering what he represents and he has achieved, FIFA could study that case."