The former Chelsea star is believed to be keen to play for a new team to prepare for the 2013 Africa Cup of Nations as Chinese Super League season has finished.
“The FIFA administration services are looking into it,” FIFA said in a statement.
It is not known whether Drogba has a club lined up to move to, but he has been linked with a move back to Marseille, the club he left for Chelsea in 2004, as well as Liverpool, the BBC said.
Drogba joined Shenhua in June on a two-and-a-half-year deal after helping Chelsea to the Champions League title.
The 2013 Africa Cup of Nations will be held in South Africa between January 19 and February 10.
Meanwhile, the five candidates for the BBC African Footballer of the Year 2012 award have been revealed adds the BBC.
Yaya Toure has made the shortlist for the second consecutive year and he is joined by his Ivory Coast team-mate Didier Drogba, Senegal’s Demba Ba, Morocco’s Younes Belhanda and Zambia skipper Christopher Katongo.
The winner will be decided by African football fans, which have until December 13 to vote through a text service.
Drogba could not have bid a better farewell to Chelsea at the end of the season after scoring the winning penalty to clinch the Champions League trophy for the first time in the club’s history, and also scoring what proved to be the winning goal in the FA Cup final.
His Ivorian compatriot, Toure, was a key player for Manchester City as the Sky Blues were crowned Premier League champions for the first time – and their first top-flight title for 44 years.
A domestic title was also earned by Belhanda, whose 12 goals and all-round performances were a huge factor as Montpellier pulled off a major surprise to win the French Ligue 1 championship.
On the international scene there was yet another first as Katongo led from the front for Zambia, skippering them to a shock victory in the Africa Cup of Nations, where Chipolopolo beat Ivory Coast on penalties in the final.
Ba fared less well at the Nations Cup, with Senegal going out of the competition at the group stage, but he enjoyed personal success with Newcastle where he ended last season as the club’s top scorer with 17 goals, helping them to finish fifth in the table.