The BBC's debate would take part on Sunday 9 December, two days before MPs are due to vote the government's Brexit deal.
In his article, Mr Gyimah said that if MPs were to support the agreement it would "set ourselves up for failure" by surrendering "our voice, our vote and our veto".
Brexiteers have accused the government of betraying the 2016 referendum, as the deal could see the United Kingdom locked in the EU customs union long after the article 50 deadline.
But in a tweet on Saturday, Mr Corbyn said: "Theresa May said she wanted a head-to-head debate with me on her botched Brexit deal and I am ready to do that".
"The day after the prime minister's stage-managed visit to Scotland, during which she failed to engage with any politicians or individuals who oppose her proposals, this unique and positive cooperation between four of the five parties at Holyrood indicates Scotland's strength of feeling on Brexit and the prime minister's untenable position, as well as illustrating the isolation of the (Conservatives) on this matter", they said in a joint statement.
Meanwhile Labour shadow chancellor John McDonnell has said if there was a second referendum then remaining in the European Union would be one of the options. Since then, it has been more and more hard to agree on bigger political issues.
"The bottom line is that we must not end up with a no deal by default".
Jeremy Corbyn has yet to confirm if he will take part in the debate
"In relation to Mr Khashoggi, we want to see a full and transparent investigation of what happened and those responsible being held to account".
The Bank of England also warned that leaving without a deal would trigger a financial crisis.
May said if her plan was voted down by parliament the government and businesses would have to make decisions about implementing preparations for no deal.
Shadow cabinet sources said that, while it was entirely right that Labour should focus on defeating May's deal and trying to force an election, there was wide acceptance that it was unlikely to achieve that goal, so the party would soon be unable to argue that it could negotiate a better deal than May.
Some lawmakers urged May to return to the European Union for better terms.
"If this deal is rejected in the Commons we are left with, as was already stressed a few weeks ago by Prime Minister May, an alternative: no deal or no Brexit at all".
"I ask every member of Parliament to think about delivering on the Brexit vote and doing it in a way that is in the national interest and doing it in a way that is in the interests of their constituents because it protects jobs and livelihoods".
The shadow cabinet alliance pushing Labour to prepare for the option of a second public vote includes Brexit spokesman Keir Starmer, deputy leader Tom Watson, shadow Northern Ireland secretary Tony Lloyd and Richard Corbett, the leader of Labour MEPs in the European parliament. She said Britain would develop its own sat-nav system, at an estimated cost of several billion pounds (dollars).