"Any debate must involve someone who believes in Brexit & the British people being fully in control of their laws, rather than giving back control to the European Union like the PM's deal".
This would be the first time May has been willing to go head-to-head with 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.
"The prime minister has given up, she is saying this is where we are and we just have to accept that", Democratic Unionist Party leader Arlene Foster told the BBC.
But with almost 100 Conservative MPs now saying they oppose the deal, Downing Street risked sparking outrage on the Government's own benches by inviting Labour MPs to a briefing on the deal, in the hope of winning over parliamentarians representing Brexit-voting districts.
"This is a really important moment for our country".
As Mrs May heads for Wales and Northern Ireland on Tuesday to try and sell the deal as "good for the union", she told The Sun: "I am going to be explaining why I think this deal is the right deal for the United Kingdom - and yes, I am ready to debate it with Jeremy Corbyn".
Labour is also behind plans for a head-to-head before the December 11 vote, saying Mr Corbyn would "relish" going up against the Prime Minister over the Withdrawal Agreement. These are at odds with the referendum mandate of taking back control.
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It has been reported a debate could clash with the finale of the jungle-based reality television programme, now starring Noel Edmonds and Harry Redknapp.
But the Labour leader said Mrs May had brought home a "botched deal that was a bad deal for the country" and that "ploughing on is not stoic, it is an act of national self-harm". It is a big decision MPs will be taking. "I believe this is in the national interest".
"What I think is important is that people are able to see the issues around this plan".
She said: "As it now stands, the majority of people in this House will not vote in favour of the Prime Minister's deal, despite her very best efforts, so she needs Plan B".
Meanwhile, Scotland's First Minister Nicola Sturgeon put herself forward as someone who would speak against leaving the European Union in a TV debate.
BORIS Johnson has pitched to be part of the Brexit TV debate - blasting Jeremy Corbyn and Theresa May because they are both Remainers.
"If you're confident in your position there should be nothing in that that worries you".