The First Minister said he will take on "all and sundry" in the debate about the future of Scotland but wants to take on Mr Cameron first.
The Prime Minister has repeatedly said that the debate should take place among the people of Scotland, pointing to Scottish MP and Better Together chief Alistair Darling as the key speaker for the Unionist campaign, but Mr Salmond has indicated that he is yet to take no for answer.
"Let's see where the Prime Minister can hide on this one," he told BBC Radio Scotland. "I'm hoping we can box the Prime Minister into a corner, and let me explain why I think he has to do it.
"The Prime Minister says on the one hand, 'I'm not going to take part in the debate because this is a matter for the people of Scotland'. On the other hand he sends himself, and also the Chancellor of the Exchequer, the Defence Secretary, Westminster committees and reports (to Scotland). The Conservative party are dictating the agenda of these committees.
"He wants to dictate the terms of the independence debate without being subject to the responsibility of open debate and democratic scrutiny.
"Now that seems to me an impossible position for the Prime Minister to defend, so he has two choices. Either he can stay out of the debate or, alternatively, if he wants to continue in the debate then there has to be a first debate between the First Minister of Scotland and the Prime Minister in London.
"Then we will be able to take on all and sundry."
Deputy First Minister Nicola Sturgeon said yesterday that there is "no question" that Mr Salmond will debate with Mr Darling and new Scottish Secretary Alistair Carmichael between now and the referendum, but it is unclear if these debates would be televised.