Sturgeon leads the left-wing Scottish National Party (SNP), which is viscerally anti-Conservative.
But a leaked memo in The Daily Telegraph newspaper said Sturgeon had told France's ambassador to Britain that she wanted Cameron to remain prime minister after the May 7 general election.
The SNP has indicated it would be prepared to back a minority government of Ed Miliband's centre-left Labour Party, on a vote-by-vote basis, to keep Cameron's centre-right Conservatives from power.
The Telegraph said the note was written by a senior British civil servant following a confidential conversation with Pierre-Alain Coffinier, the French consul-general in Scotland, regarding the meeting.
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The memo said: "Discussion appears to have focused mainly on the political situation, with the FM stating that she wouldn't want a formal coalition with Labour; that the SNP would almost certainly have a large number of seats... That she'd rather see David Cameron remain as PM (and didn't see Ed Miliband as PM material)."
However the civil servant appeared to doubt whether this accurately conveyed Sturgeon's meaning, adding: "I'm not sure that the FM's tongue would be quite so loose on that kind of thing in a meeting like that, so it might well be a case of something being lost in translation."
A spokesman for the embassy also denied the story.
"Ms Sturgeon did not tell the French ambassador about her personal political preferences with regards the future PM," he said.
Coffinier confirmed he had spoken to the British government's Scotland Office, but denied saying Sturgeon had voiced a preference about the election outcome.
He told AFP: "The political situation in Britain was indeed discussed during the meeting between the French ambassador and the Scottish first minister at the end of February and I gave a report of it in general terms.
"However, at no stage was a preference expressed about the result of the forthcoming British general election."