Mexico’s Central Bank Governor Agustin Carstens and his Kazakhstan counterpart Grigory Marchenko are also in the running.
The post became vacant when Dominique Strauss-Kahn quit last month over sexual assault charges in New York.
China, India, Brazil and Russia have called for an end to the tradition of European countries heading the IMF, as their economies are now becoming more important in the global economy.
Meanwhile, Ms Lagarde is facing allegations that she abused her authority in 2008 when she granted a large payout to a prominent businessman to settle a legal case.
The final selection for the head of the IMF is expected to be announced by the 30th of this month.