On Thursday evening Downing Street made a dramatic "final offer" to broadcasters, saying Cameron will sign up only to one 90-minute contest involving at least seven party leaders to be held before the campaign formally begins on March 30.
Labour accused the prime minister of running "scared" of Miliband and accused him of an "outrageous attempt" to "bully" the broadcasters.
Speaking on LBC radio this morning, Clegg said he would step in."If David Cameron is too busy, or too important, to defend the record of this government, I offer myself. I'll do it instead," he said. "I'm very happy to do it."
Cameron's latest terms for taking part have been set out in a letter from his director of communications, Craig Oliver, to Sue Inglish, chairwoman of the broadcasters' leaders' debates committee.
It states: "In order to cut through this chaotic situation I am willing to make the following proposal: There should be one 90-minute debate between seven party leaders before the short campaign.
"As well as the Prime Minister, the leaders of the Green Party, Labour, Liberal Democrats, Plaid Cymru, SNP and Ukip should invited.
"The leader of the DUP should be allowed to make his case for why he should be involved. If the broadcasters cannot agree amongst themselves who hosts the debate, lots should be drawn, though the debate should be freely available to whoever wants to broadcast it.
"In order for it to be organised in time, the debate should take place during the week beginning March 23. I will make myself available to negotiate the details. Having been the editor of numerous broadcast news and current affairs programmes, I know this is ample time to organise a programme.
"This is our final offer, and to be clear, given the fact this has been a deeply unsatisfactory process and we are within a month of the short campaign, the Prime Minister will not be participating in more than one debate."
Deadlock over the debates prompted Sky News and Channel 4 earlier to offer to host a head-to-head clash between the Prime Minister and the Labour leader on a date of the politicians' choosing, and Miliband said he was prepared to take part "any time, any place, anywhere" in an attempt to force the premier's hand.
Douglas Alexander, who is leading Labour's general election strategy, said: "We continue to support the broadcasters' proposals, including for seven-way debates alongside a two-way debate.
"But this is an outrageous attempt from the Prime Minister to bully the broadcasters into dropping their proposals for a head-to-head debate between David Cameron and Ed Miliband.
"That it comes only hours after Ed Miliband called David Cameron's bluff and said he would debate him any time, any place, shows the lengths David Cameron will go to run scared of a debate with Ed Miliband."