The Foreign Secretary said MPs should be "able to air their views" after Jacob Rees-Mogg was criticised for saying the Prime Minister must deliver the Brexit she promised or risk collapsing her Government.
It was described as a tense meeting, the BBC's Norman Smith said.
Ministers have been involved in heated discussions recently as they tried to choose between two earlier models.
But speaking on the BBC's Daily Politics, Mr Rees-Mogg hit out at suggestions the new arrangement could, in a bid to ensure smooth trading, involve a single market on goods with the European Union and close alignment with its regulations. "At Chequers (Mrs May) must stick to her righteous cause and deliver what she has said she would, she must use her undoubted grace to persevere".
Simon Hoare, MP for North Dorset, took to Twitter to tell Rees-Mogg: "The hectoring nonsense / blackmail has to stop, the reality of parliamentary arithmetic dawn and the calamity of a Corbyn Government woken up to". But May has struggled to unite pro- and anti-Brexit camps in her cabinet and party around a plan for future trade with the EU.
But MPs who voted to sever ties with Brussels fear the PM could be about to compromise on her red lines in a bid to bring the disparate factions of her cabinet into line behind a common position.
The EU has rejected previous British proposals for trade with the bloc after Brexit, saying Britain can not both quit the EU and retain the main economic benefits of membership.
May, who leads a minority government dependent on the support of a small Northern Irish party, has ruled out staying in the EU customs union, which groups EU members in a duty-free area where there is a common import tariff for non-EU goods.
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Speculation has been mounting that the prime minister will set out plans for a soft Brexit in order to overcome the problems at the Irish border and ports across the United Kingdom if there were customs or regulatory barriers to trade.
Asked about the possibility of people quitting as ministers after Friday's showdown, Mr Gove said: "The only departures that I think we will see are more departures from Heathrow when a third runway is built".
Ms Jenkyns told the ConservativeHome website: "If we don't deliver Brexit, if we're half in and half out, it's going to be catastrophic for the Conservative Party".
"They're not going to trust the party".
He insisted he was "confident" May would deliver the Brexit she had promised, but warned the PM that backsliding could result in splitting the party like Sir Robert Peel, who plunged it into the political wilderness for almost three decades following bitter divisions over trade reforms.
But Cabinet ministers have been kept in the dark about any new proposal ahead of Friday's meeting.
"We know some of you want to be the future party leader".