It follows reports that Mr Cameron could take part in a pre-election TV debate with Ukip leader Nigel Farage as part of a series of broadcast showdowns in the run-up to the 2015 General Election.
The Sunday Times reported that the Prime Minister was open to a ''2-3-5'' format drawn up by his aides.
Under the plan, Mr Cameron would hold one head-to-head debate with Labour leader Ed Miliband - as the other potential prime minister - a second, which would also include Liberal Democrat leader Nick Clegg, and a third with Mr Farage and the Green party leader Natalie Bennett.
Deputy First Minister Nicola Sturgeon said: "It's astonishing that David Cameron is happy to have a head-to-head debate with Nigel Farage - whose party doesn't have a single seat in the House of Commons - but continues to run scared of a debate on the future of Scotland with First Minister Alex Salmond.
"We now know he is happy to debate with the leader of Ukip who constantly lose their election deposits in Scotland, but is not willing to debate with Scotland's democratically elected First Minister. That begs the question what is he afraid of?
"It was reported on Saturday that the Prime Minister is to visit Scotland more often over the next few months in order to campaign for a No vote. Why on earth is he not happy to publically debate his position? Given he is now happy to debate (with) a wide range of politicians in England, the Prime Minister should stop snubbing Scotland."
Mr Cameron has repeatedly ruled out facing Mr Salmond live on television, insisting the debate is for the people of Scotland.
Responding to Ms Sturgeon's comments, No 10 pointed to a letter which the Prime Minster wrote to Mr Salmond last autumn.
Mr Cameron wrote: "I have already made clear - and will continue to do so - that it is not me you should be debating with head-to-head on TV, but Alistair Darling."
He added: "Separation would be forever, not just for the length of a five-year term. The referendum is therefore too important to be reduced to the status of some glorified General Election.
"People should cast their vote in the knowledge that they are deciding not just for themselves, but also for their children, grandchildren and succeeding generations.
It is for people in Scotland to decide. And it is right for you and Alistair Darling - as the leaders of the respective campaigns, with votes to cast as well as votes to win - to debate head-to-head on TV."
Responding to the report in The Sunday Times, a No 10 source said: ''It is speculation on what might happen in talks that are not going to happen for several months.
''We have not ruled anything in or out, so that means people can speculate what might happen in the talks.
''But the reality is these talks are several months away.''