French Finance Minister Christine Lagarde and Governor of the Bank of Mexico Agustin Carstens will fight it out for the top job.
The post became available after the former head of the IMF Dominique Strauss-Kahn resigned.
Mr Strauss-Kahn was arrested in the US last month on charges of an alleged sexual assault.
He has denied the charges.
The IMF said it expects to complete the selection process by 30 June.
"The Executive Board will meet with the candidates in Washington DC and, thereafter, meet to discuss the strengths of the candidates and make a selection," the fund said.
Ms Lagarde is considered by many as the front runner for the post.
She is backed by the European Union and in recent days she has also won the support of Egypt, Indonesia, and the United Arab Emirates.
Mr Carstens has the support of Latin American countries.
However, he acknowledged that his rival had the edge in the race.
"I'm not fooling myself. It's like starting a soccer game with a 5-0 score," Mr Carstens said during an appearance at the Peterson Institute for International Economics on Monday.
However, Mr Carstens said that if a European candidate is appointed to the post, it may result in a conflict of interest, given the ongoing debt-crisis in some of the European countries.
"We could have a situation where borrowers dominate the institution," he said.
Mr Carstens said that the European debt-crisis had snowballed into a big problem over the years and the region needed a fresh perspective in order to solve the problem.
"What will help me is precisely to have a fresh pair of eyes," he said.
"Also someone coming from the outside can in a way speak of their mind more frankly and I think that will be an advantage," he added.
Ricardo Ochoa, head of international affairs at Mexico's finance ministry, said that Mr Carstens' experience as the head of the country's central bank, would allow him to be more sensitive to the problems of countries which needed IMF aid.
"He has been on the other side of the table," Mr Ochoa told the BBC.
"Mexico already has been in the situation where important reforms have to be implemented, and I think that puts him in a situation - to have a more understanding and more sensitive IMF," Mr Ochoa added.
The International Monetary Fund (IMF) has shortlisted two candidates to take over as its managing director.