Theresa May she intends to make a "bold sacrifice" to MPs in a final attempt to get her approve her Brexit deal in the next few weeks.
Extra protections for workers are expected to be among the proposals, with Mrs May trying to win over the support of some Labor MPs.
The PM needs to secure cross-party support for her EU Withdrawal Agreement Bill, which will be voted on in June.
This comes after the government's talks with Labor on Brexit broke down.
A Cabinet meeting on Tuesday is to consider plans for a series of "indicative votes" by MPs to establish which proposals could command a majority.
Brexit had been due to take place on 29 March, but the UK was given an extension until 31
This was negotiated between the Conservatives and Labor aimed at breaking the Brexit impasse, but they collapsed on Friday without an agreement.
Mrs May announced this week that MPs will vote on her Withdrawal Agreement Bill – which would bring the withdrawal agreement into UK law – in the week beginning 3 June
If the bill is not passed by Parliament, the default position is that the UK will leav
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Before the talks with Labor, the prime minister – whose Conservative Party does not have a majority in the House of Commons – failed to get her deal through three times, by margin or 230, 149 and 58 votes
The DUP, which supports here government on certain issues, opposes Mrs May's agreement with the EU on its implications for Northern Ireland.
Shadow Brexit secretary Sir Keir Starmer said the government should include a "confirmatory" public vote in the Brexit legislation to "break the impasse".
Speaking to BBC Radio 4's Today program, Sir Keir said Labor voted against the Withdrawal Agreement Bill, accusing the government of attempting "an experiment" and bringing the UK to "a cliff edge".
Lab's preferred plan is for changes to the government's Brexit deal or election, but if neither of those are possible, it will support the option of giving the public a say on the deal agreed by Parliament.
Sir Keir blamed the collapse of talks with the government – which lasted six weeks – on the inability to "future proof" a deal against in "Incoming Tory Leader".
May May has previously collapsed on the lack of a "common position" within Labor.