The experienced attacker is hoping to secure a loan move away from his current club before the winter transfer window opens
The Chinese league season came to an end earlier this month, and Drogba has set his sights on a temporary move away from Shenhua to maintain his fitness until the Afcon kicks off on January 19, 2013, with world football's governing body considering the former Chelsea star's request.
Fifa said to Goal.com: "We can confirm that the player Didier Drogba has submitted a request for authorisation to be registered outside an open registration period for a club on a loan basis.
"Our services are currently looking into the matter. As a result, for the time being, we are not in a position to further comment on the issue."
Drogba has recently been linked with clubs such as Juventus and Chelsea, but he would be unable to move before January 1 under current Fifa regulations.
Cote d'Ivoire have been drawn alongside Tunisia, Algeria and Togo in Group D of the 2013 Afcon. They take on Togo on January 22 in their first match of the tournament.