French Finance Minister Christine Lagarde and Bank of Mexico Governor Agustin Carstens are short listed by the International Monetary Fund to take over as its managing director.
The post became available when Dominique Strauss-Kahn resigned after he was arrested in the United States on 14 May on charges of sexual assault. He has denied the charges.
The IMF said it expects to complete the selection process by 30 June. Its
executive board will meet the candidates in Washington DC.
The BBC reports Ms Lagarde is considered by many as the front runner for the post.
She is backed by the European Union and also has the support of Egypt, Indonesia, and the United Arab Emirates.
Mr Carstens has the support of Latin American countries. However, he acknowledged that Ms Lagarde 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 on Monday.