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 Jan. 19, 2013, with world football's governing body considering the former Chelsea star's request.
"The FIFA administration services are looking into it,'' FIFA said in a statement.
Drogba has recently been linked with clubs such as Juventus and Chelsea, but he would be unable to move before Jan. 1 under current FIFA regulations.
Cote d'Ivoire has been drawn alongside Tunisia, Algeria and Togo in Group D of the 2013 AFCON. It takes on Togo on Jan. 22 in its first match of the tournament.
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