 Mr Strauss-Kahn is in pole position, many observers believe |
French President Nicolas Sarkozy wants former finance minister Dominique Strauss-Kahn to succeed the retiring Rodrigo Rato as managing director.
But reports have suggested Italy and Poland could put forward rival names.
By tradition, the head of the IMF is a European but many developing countries favour a fully open process.
French momentum
The IMF provides financial assistance and advice to many of the world's poorest countries and is charged with maintaining global financial stability.
Like its counterpart the World Bank, the organisation has come under attack from poorer countries which claim that it is dominated by a handful of powerful nations and that its economic solutions are too rigid and prescriptive.
Political manoeuvring over the top job has intensified ahead of a meeting of eurozone finance ministers on Tuesday.
Officials are expected to discuss potential candidates for the job but are unlikely to reach any agreement on which name will be put forward to the IMF's board.
Paris has sought to build momentum behind Mr Strauss-Kahn, an experienced politician who failed to secure the Socialist Party's nomination for president earlier this year.
President Sarkozy has already told US President George W Bush of his strong support for Mr Strauss-Kahn.
Mr Strauss-Kahn has won the backing of a number of EU countries including Luxembourg.
"Dominique Strauss-Kahn has all the qualities you need in order to become managing director of the IMF," its Prime Minister Jean-Claude Juncker said.
Other contenders
But some countries are believed to be worried about France heading the IMF at a time when its officials hold the top jobs at the European Central Bank, the World Trade Organization and the European Bank of Reconstruction and Development.
Germany's deputy finance minister, Thomas Mirow, said Mr Strauss-Kahn's credentials were not in dispute but added that there were likely to be other candidates.
Other names in the frame, according to reports, include former Dutch finance minister Gerrit Zalm, former Polish central bank governor Leszek Balcerowicz and current Italian finance minister Tommaso Padoa-Schioppa.
One potential contender to rule himself out is Italian central bank governor Mario Draghi.
Mr Draghi said he was "not interested" in the job.
Mr Rato is standing down early in October for personal reasons.