The fallout from a Greek debt default can be contained if European leaders reached an agreement to let the restructuring take place in an orderly manner, former IMF chief economist Raghuram Rajan said on Wednesday.

Euro zone ministers failed on Tuesday to reach an agreement on how private holders of Greek debt should share the costs of a new bailout.

The lack of a deal pushed bond yields of Greece, Ireland and Portugal to their highest levels since the introduction of the euro in 1999, and Moody's on Wednesday placed France's top three banks on review for a possible downgrade, citing the banks' exposure to Greek debt.

One of the advantages of this long drawn-out crisis resolution process is that many private sector entities that were exposed to Greece have reduced their exposure, Rajan told reporters on the sidelines of an investment conference in Singapore.

The extent to which banks in Europe are exposed to Greece is much more limited than it was, even say, six months or a year ago, and so the cost of a Greek default and restructuring could be absorbed by the banking sector, he said.

Rajan said a restructuring of Greece's debt looked increasingly probable as Athens lacked the political will to carry out widespread privatizations of state assets and budget tightening.

If it (the debt restructuring) happens in a way that banks and markets are prepared for, even if not publicly but at least privately, it is very well containable, he said.

But a restructuring which happens because the dialogue breaks down will be more complicated because that would suggest that there will be implications for Ireland, for Portugal and so on, and that could be more problematic down the line.

Rajan is now a professor at the University of Chicago's Booth School of Business and an economic adviser to India's prime minister.

(Reporting by Kevin Lim; Editing by Kim Coghill)