A spokesman for the First Minister said they would give "due consideration" to an invitation from the BBC to take part in a TV clash with the Better Together leader on August 12.
Mr Salmond has accepted an invitation from STV to take on Mr Darling on August 5, his spokesman said.
But the Better Together campaign said it was "disappointed" that the STV debate would not take place on July 16, as the broadcaster had originally planned.
The First Minister has repeatedly insisted he should debate with David Cameron over Scotland's future in the UK ahead of September's independence referendum, although the Prime Minister has consistently refused to do so.
Deputy First Minister Nicola Sturgeon indicated at the weekend that "should the Prime Minister continue to duck this debate, the First Minister is willing to take on Alistair Darling as the Tories' nominated substitute".
Broadcaster STV wrote to both Mr Salmond and Mr Darling last week, asking them to appear in front of an audience of 500 at the Assembly Rooms in Edinburgh on July 16.
Better Together said it had accepted that offer, with a spokesman for the campaign saying: "We are disappointed that STV have now repudiated their own date after Alex Salmond refused to take part, despite the First Minister indicating publicly that he was free that day.
"We accepted the original offer from STV in good faith, with a date that was not of our choosing or Mr Salmond's choosing. The public want to see this debate, we want this debate to happen and if STV are willing to enter into serious discussions with both, rather than just one of the campaigns, we are of course willing to talk."
The spokesman said: "We have agreed to a BBC debate with Alex Salmond on August 12. As far as we understand Alex Salmond has yet to agree to that debate. We are glad the BBC have begun serious discussions with both sides."
But he asked: "Will Salmond now accept the BBC debate on August 12?"
A spokesman for the First Minister said: "We have only received a formal invite from the BBC today, and will give it due consideration."
He stated: "We will continue to pursue a debate with David Cameron but in the meantime have accepted STV's proposal for a debate between the First Minister and Alistair Darling on August 5
"Mr Darling is on record as saying he would debate with the First Minister 'anytime, anywhere' - it now seems that was bluff and bluster and it is 'any time' except the one suggested.
"Rather than attacking impartial broadcasters, the No campaign should accept the challenge and have the debate on August 5 on STV, who have proposed a serious and substantial two-hour debate involving a 500-strong audience of ordinary people representing public opinion across Scotland."