Scotland's former first minister threw down the gauntlet to the Ukip leader during an interview on the Sky News Murnaghan programme.
The SNP's foreign affairs spokesman said he would be "delighted" to take on Mr Farage "or any comer on the anti-European side".
He told the programme: "I don't know if they've quite decided who they will be fielding yet. They seem to have spent a lot of time fighting with each other.
Alex Salmond (above) threw down the gaunlet to Nigel Farage (below)
"That's the sort of folk they are. But yes, of course you debate all comers in a referendum campaign.
"If I may say so it has been Mr Cameron who's been tentative and sensitive about debating with people in recent history."
A Ukip spokesman later said Mr Farage was "absolutely up for it" but that any debate should be broader than just a one-to-one with Mr Salmond, The Press Association reports.
He said: "Mr Salmond is no longer leader of the party, no longer leader in Scotland, no longer leader in Westminster and it should be broader than just Nigel and Salmond, because neither of them represent the whole argument."
Mr Salmond, who stood down as first minister and SNP leader after the No vote to Scottish independence in 2014, also told the programme that the Prime Minister would have no choice but to resign in the event of a vote for Brexit.
He said: "He won't have a choice in the matter. If he loses the referendum then he'll be shown the door as indeed will the Chancellor George Osborne.
"It's untenable to try and maintain a position if you lose a referendum and, what is it they used to say in the Conservative Party a long time ago, you would have to do the honourable thing."
Mr Salmond has branded Mr Cameron's EU renegotiation a "sham" and accused both sides in the debate of scaremongering.
He said: "If we have that sort of debate over these next few weeks then I think there's a very real chance that the anti-Europeans will win.
"If we have two campaigns that are scaremongering then in that case the biggest fearmongering tends to win.
"The real danger is that the pro-European case, the real case about this country's position in Europe is not being made."