Drogba has been strongly linked with a move away from Stamford Bridge this summer, despite the Ivory Coast international claiming he does not want to leave the Blues.
Drogba's agent Pierre Frelot has reiterated that the former Marseille man is happy at Chelsea, but has hinted that he could be interested in a move to Real.
"Why Not," Frelot said in the Daily Mirror when asked about the possibility of Drogba moving to the Bernabeu.
"Didier is calm because he is at a great club like Chelsea, but Real Madrid are also a great club."
Chelsea are reportedly chasing Real Madrid's Brazilian international Robinho and the news could open up a possible swap deal for Drogba.