The former foreign secretary turned vocal backbench Tory critic of the Prime Minister stopped short of putting himself forward to challenge her in a live broadcast.
Her plan faces opposition from both eurosceptics and europhiles among her party's 314 lawmakers and around 313 lawmakers from opposition parties.
But No10 has said that other political leaders are not part of the planned debate.
The revised version of Scotland's Place in Europe published yesterday includes economic analysis, first published in January, which suggests the free trade expected under the Mrs May's withdrawal proposal could leave Scottish GDP about £9 billion lower by 2030 than if the country had stayed in the European Union - the equivalent of £1,600 per person. "We can back this deal, deliver on the vote of the referendum and move on to building a brighter future of opportunity and prosperity for all our people".
"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".
"The Brexit deal has been agreed and I am taking that to the House of Commons", she said during the visit.
"I am willing to stand up and explain why I think it is the best possible deal available for the United Kingdom".
"If the deal is voted down in the House of Commons, it will lead to more division and more uncertainty".
"What I think is important is that people are able to see the issues around this plan".
While Mrs May continues to appeal directly to voters to support her plan, some questioned whether she would not have been better off remaining in Westminster trying to win over MPs who will decide whether to back the agreement in the vote on December 11.
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In their apology clip, the designers didn't repeat an earlier allegation that their Instagram accounts were hacked. China has risen, and it's no longer a place for you to simply take our money and leave without showing respect".
Labour Brexiteer Gisela Stuart also attacked the proposed line-up, saying it was limited to "two politicians who voted and campaigned for Remain".
Trump said the deal struck with Brussels "sounds like a great deal" for the EU. British negotiators could ask for the deal to be tweaked to make it more palatable to British MPs.
He added: "When you meet them - and I met last week with a prominent Japanese company - they indicate that decisions on investment, for example being driven in Japan, by their head offices are decisions that are now very hard to get concluded".
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.
"I think we have to take a look at, seriously, whether or not the U.K.is allowed to trade, because you know right now, if you look at the deal, they may not be able to trade with us", he said. "I believe this is in the national interest".
The Department for Exiting the European Union said it does not comment on leaks.
"We hear anecdotal evidence every day of universities finding it harder to recruit people from other European countries because they've already decided to make judgments about what they're hearing and feeling about the Brexit process, so there is, I think, growing evidence of the adverse impact this kind of deal will have".
Mrs May has clashed with First Minister Nicola Sturgeon ahead of the visit.
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".