According to Reuters, the French finance minister seems to have enough support from key officials to take the position after it emerged that Russian prime minister Vladimir Putin and a number of other European Union members said they thought she was the best candidate for the job.
The role was vacated by Dominique Strauss-Kahn earlier this year and Ms Lagarde has long been thought of as favourite to succeed him, although Mr Carstens, governor of Mexico's central bank, recently emerged as an alternative candidate.
Recently, it was reported by Bloomberg that Ms Lagarde will be backed by the US in the IMF leadership contest.
The world's primary superpower believes in the "unwritten rule" that the World Bank be led by an American and the IMF be headed by a European.
By Asim Shah