"It mustn't be an option between frying pan or fire - but it is now incumbent on all of us who oppose that false choice to propose a workable alternative".
Leadsom and Gove are holding talks with three other Cabinet ministers, including International Development Secretary Penny Mordaunt, who has indicated she may quit her ministerial post over the plan.
One pro-Brexit Conservative lawmaker, Simon Clarke, urged wavering colleagues Monday to join the rebellion, saying "it is quite clear to me that the captain is driving the ship at the rocks".
The required number represents 15 percent of the Conservative MPs.
It is also unclear what would happen if Parliament rejected the deal when it is put to a vote, likely next month.
The DUP, which props up the government, said it was sending the PM a "message" over her plan to "separate" Northern Ireland from the rest of the UK. Without the DUP, May's Conservatives no longer command an automatic majority in the Commons and could be at risk of defeat in a no-confidence vote.
It would be one way out of her bind if the deal is voted down, but the PM has repeatedly ruled out going back to the public to ask for their say on the deal, and her Leave-supporting critics feel the same way.
Shocked Cheryl addresses negative reaction to X Factor performance
Several articles have been written about the singer since her performance on the show. Pic on right was me before I just happened to sit down.
If the EU approves the deal it needs to be passed by the European and British Parliaments - where the parliamentary arithmetic looks daunting for May.
Diplomats' lives in Brussels are now a combination of missed meals, late nights, meetings and speculation about the state of the British government, says Adam Fleming, who is on a similar schedule.
The EU's Brexit negotiator Michel Barnier said on Monday that the EU had yet to decide on any extension to the envisaged transition process. It is due to end in December 2020 but can be extended by mutual agreement if more time is needed.
"I think it is important that in delivering for the British people we are out of the implementation period before the next general election", May said at the annual conference of a United Kingdom business organization, the Confederation of British Industry.
The UK government has indicated that after Britain has formally left the European Union, workers from any part of the world will be subjected to similar visa rules. She said that, after Brexit, EU nationals can't "jump the queue ahead of engineers from Sydney or software developers from Delhi". But some are unhappy with the immigration plans, which have yet to be revealed in detail.
May has drawn widespread criticism for comments made in a speech to the Confederation of British Industry (CBI).
"The prime minister is trying to take us into a blindfold Brexit, a deal created to get her through to the next stage of the process without anyone being able to see where we're heading", he said.