Sarkozy held a private conversation with the U.S. president during a G20 summit last Thursday that was captured on a communications system by journalists who reported that the French leader had branded Israeli Prime Minister Benjamin Netanyahu a "liar.
In another part of the same conversation, heard by a few radio journalists, Sarkozy also vented his frustration over the unexpected Papandreou decision to call the now-abandoned referendum, telling Obama it was not worth laying in to a man who was already down.
The conversation was cited on Greek blog sites.
The White House had no immediate comment on the report, nor did the Elysee press department in Paris. The Greek prime minister's office, in response, referred to telephone consultations on Wednesday morning between Papandreou and Sarkozy on attempts to form a government.
Reuters, which had a journalist among those who heard the comments about Netanyahu, did not hear the part devoted to Papandreou but contacted two other journalists for their accounts of what was said.
Those accounts differed on some of the precise wording but both said Sarkozy had spoken of a "madman Papandreou" and added that there was no point in laying into him over the referendum plan as he was "depressed."
Papandreou caused consternation among European leaders last week by abruptly calling a Greek referendum on a euro zone deal he had struck hours earlier with euro zone leaders about a financial rescue of Greece in return for further austerity measures.
The call was abandoned shortly afterwards. Papandreou is standing down as Greece seeks to form a government of national unity and appoint a new prime minister.