Downing Street also stepped up the campaign in Parliament, writing to MPs with an explicit warning that voting against the deal could result in a second European Union referendum that reverses Brexit.
Asked today whether she had considered holding a bushtucker trial instead, May replied: "I think this is an issue on which we want to debate the questions of our future".
The prime minister rejected claims from Democratic Unionist Party leader Arlene Foster that she had "given up" on getting a better Brexit deal.
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".
"I have a clear deal that I believe is in the interests of the United Kingdom and I think it is right for people to hear what Jeremy Corbyn's views are as those have been a little uncertain recently about exactly where he stands".
She said she would prove: "I have got a plan, he hasn't got a plan".
Speculation about the party's position has been stoked by a report in The Sunday Times that shadow chancellor John McDonnell held talks with Tom Baldwin and Alastair Campbell, former spin doctors to Ed Miliband and Mr Blair, who are now campaigning for a so-called People's Vote.
Jeremy Corbyn’s joke at Theresa May’s expense triggered laughter on the Labour benches
She added: "Exactly how it might be done, if he takes it up, would be a matter for the broadcasters to determine". It is a big decision MPs will be taking.
"I believe that it is important that when people come to that vote, they consider the interests of this country, they consider the interests of their constituents, and they consider the importance of delivering on Brexit", May told MPs.
The SNP's Iain Blackford said the agreement was "full of ifs and buts" which would result in Scottish fishermen being "sold out" while the Lib Dem leader Sir Vince Cable called for another referendum.
She said: "The danger is a debate between Theresa May and Jeremy Corbyn is simply a debate between two versions of Brexit which are only really different around the margins".
Challenged on BBC's Andrew Marr Show about the prospect of an election being unlikely, Mr Burgon said: "I think the age of the experts is over".
European Union leaders will have to weigh up if they still want May to win, and how badly they want to just move on.
The Labour boss has said he would "relish" the chance for debate - but would wait until a formal invite comes in first.
"If you're confident in your position there should be nothing in that that worries you".