The Prime Minister is considering her next move to break Brexit's stalemate following the recent defeat of her withdrawal plan.
According to government sources, reaching Theresa May's deal through the lower house is "ambitious."
But MEPs will again vote on alternatives with a customs union on Monday The EU considers MEPs the most likely option for MEPs.
Some older Brexiteers have warned Ms. May about such a move.
The Prime Minister has until 1
2 April to seek a longer extension to prevent the UK from leaving the country A deal.
Ms. May said Britain needed "an alternative way forward" after her plan had been defeated on Friday with 58 votes after having been beaten 230 and 149 votes before.
The government has not won over 34 Co Independent Rebels, including both Remainers and Brexiteers, who claim that Ms. May's agreement is still too close to Europe.
The DUP of Northern Ireland, on which the government bases its votes in the House of Commons, continues to deal with the parliament.
But a # 10 source indicated that the Prime Minister would continue to seek support for their Brexit deal in the House of Commons, insisting that efforts "go in the right direction".
The political correspondent for the BBC, Alex Forsyth, described the Cabinet as "deeply divided" as to what to do next.
Tory Brexiter Steve Baker, who resigned as Brexit minister because of the Prime Minister's negotiation, wrote in the Sunday Telegraph that Mrs. May was not allowed to conduct the trial. "
He also said the Conservative party could split if the Prime Minister wanted a customs union with the EU, as this would "reverse the outcome of the vote."
This is one of the options this could be done by MPs of all parties in a second round of "indicative votes" on Monday
The Customs Union allows companies to move goods without controls or fees in the EU, and continued membership would prevent the United Kingdom from removing independent trade agreements after Brexit.
None of the eight proposed Options of Brexit of deputies had received on March 27, the majority of the first directives but most of the votes were a customs union with the EU and a referendum on an agreement.
Labor leader Jeremy Corbyn said his party would propose an agreement for a customs union with the EU to protect the problem of avoiding a hard border in Northern Ireland.
Leading Tory Brexitist Jacob Rees-Mogg told the Sunday Telegraph that the party must be led by "someone who has always supported Brexit".
He wrote, "Now, the Tories have the opportunity to move away from the current government position of improving a bad idea that they never believed at their highest level, to one that embraces them."