The Prime Minister is embarking on a whirlwind few days of campaigning to and lobbying MPs to back her deal to leave the EU.
On Sunday, EU leaders approved the Withdrawal Agreement and Political Declaration on future relations, which Mrs May has negotiated.
Former Brexit secretary David Davis asked why the United Kingdom was not withholding payment of the £39 billion divorce bill until after a trade deal was struck.
She will say, after chairing a meeting of her cabinet on Monday morning, that she is "absolutely" sure there is no better deal on offer.
Speaking on his LBC show, he said: "I wouldn't want to see the debate conducted by politicians".
Downing Street has, however, insisted that it was "very clear" the United Kingdom would be able to sign new trade deals.
He asked if Mrs May was aware that in signing the agreement including the backstop she was handing the European Union a "cudgel" to use against the UK.
"We have already been laying the groundwork for an ambitious agreement with the USA through our joint working groups, which have met five times so far".
Mrs May used an interview with The Sun to confirm that she was willing to join a televised debate with Mr Corbyn.
He also warned that under the deal the United Kingdom would have to "agree to demands on waters and quota shares" to get a future trade deal or extend the transition.
The timing gives Mrs May a fortnight to avert what threatens to be a humiliating defeat at the hands of scores of Conservative rebels.
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".
"Because I have got a plan".
Mrs May joked: "I'm tempted to say to her that throughout the last 18 months of these negotiations at virtually every stage people have said to me it wasn't possible for me to negotiate a deal with the EU - No sooner do I then people are saying "well what's the next thing you're going to negotiate".
The announcement followed a report by The Daily Telegraph that May was seeking a debate on the issue with the Labour leader as part of her effort to win parliamentary approval for the deal, which marks the biggest shift in British foreign and trade policy in more than four decades.