May and Jeremy Corbyn, leader of the main opposition Labour Party, are set to contest her Brexit plan on December 9 – two days before a crunch vote in the British parliament.
But they are yet to settle on which channel will brodcast the debate, wrangling over which primetime slot will draw a bigger audience, and on whether to include an audience or panel to ask questions.
The United Kingdom is set to leave the European Union on March 29 next year, even as the nation remains sceptical over the divorce agreement.
Meanwhile, smaller opposition parties such as the Scottish National Party (SNP) and Liberal Democrats are furious that they look set to be shut out from the TV debate.
The back-and-forth began after the BBC announced that Conservative leader May had accepted its debate offer, but that it was still waiting to hear back from Corbyn.
However, Corbyn said on Thursday that he favoured the commercial operator, ITV.
While the BBC had proposed that the leaders debate alongside a panel asking questions could be broadcast, Labour reportedly objected, preferring ITV’s proposal for a head-to-head format.
This would be the first time May has been willing to go up against the Labour leader in a live television debate after she refused to take part in any in the run-up to last year’s general election.
Meanwhile, SNP leader Nicola Sturgeon said it would be a “travesty of democracy” if a range of political voices were frozen out.
The SNP is the third-largest parliamentary party, with 35 seats in the 650-seat chamber.
The Liberal Democrats said it had written to the director general of the BBC, questioning the legality of excluding them from the debate. With 12 seats, they are the fourth-largest party in parliament.
Debates between leaders have become a fixture of British politics over the past decade, with months spent trying to agree on a debate format during the 2015 general election.
May came in for heavy criticism during the 2017 snap general election for dodging direct TV debates with other party leaders and sending the then-Home Secretary Amber Rudd to take part instead.
She later justified her decision, saying it was more important to take questions directly from the voters.
Ministers of Parliament in the House of Commons will vote on December 11 on the divorce deal agreed by May with the EU, with many already warning they plan to oppose it.
Appearing before a committee of legislators on Thursday, May repeated that the decision was up to parliament, but stressed that she had got “the best deal for the UK”.
After securing a deal with the EU over the weekend, May has launched a nationwide campaign to drum up support for her agreement.
The odds look stacked against May winning parliamentary approval for her deal with criticism coming from all sides, including the Northern Irish party propping up her minority Conservative government.