The Giallorossi have had injury troubles in the striking department this season, with Mattia Destro and Francesco Totti missing long stretches of the season with injury complaints.
Since arriving in Istanbul last year, the 36 year old Ivory Coast international has been in great form for the Turkish giants, scoring twenty goals in fifty appearances.
Il Messaggero report that Roma could sign the veteran striker, whose contract expires in the summer, although his €4 million salary could be an issue that Roma will have to contend with.
Drogba has netted ten goals in 23 appearances in the league for Galatasaray this season.