Bringing the EU Withdrawal Agreement Bill forward would allow the prime minister to push ahead with her ambition of delivering Brexit before the summer - despite the lack of agreement so far in the cross-party talks, said BBC political correspondent Iain Watson.
"I have talked to colleagues, some of whom voted for it last time, and they think it is dead and they will vote against it this time", Peter Bone, a Conservative lawmaker and Brexit supporter, told Talk Radio.
Brexit has been delayed until October 31 as MPs failed to reach an agreement on how best to exit the EU.
Whether this has a chance of success depends on whether enough MPs would be willing to vote for Labour's Brexit plan without it being subject to another referendum.
"The factual position is if MEPs are elected and (the British) parliament has not approved a withdrawal agreement bill which has achieved royal assent by June 30, they will take their seats", May's spokesman said.
A handout photograph taken and released by the UK Parliament on 3 April 2019 shows Britain's Prime Minister Theresa May speaking during the weekly Prime Minister's Questions (PMQs) question and answer session in the House of Commons in London.
A number of influential former cabinet ministers, including Johnson and David Davis, warned her in a letter on Tuesday to reject a customs union deal with Labour.More news: Sachin Tendulkar rates IPL 2019 as truly incredible
"Unless she can demonstrate something new that addresses the problem of the backstop, then it is highly likely her deal will go down to defeat once again".
The conversations with Labour had been "difficult", the spokesman said, but ministers were "determined to find a way through" the Brexit impasse.
She turned to Labour last month in the hope of finding a way through, but the party is insisting on a close trading relationship with the European Union that many Conservative MPs reject.
"When MPs come to look at that (bill), they will recognise that we have a duty in parliament to deliver on the result of the referendum and deliver Brexit", she said.
The bill would need to get through all its different stages before recess, which is why the week of 3 June has been set, coming after the European elections and parliament's Whitsun recess.
Allies of the Prime Minister attempted to calm Tory fears about the prospect of a damaging split in the party over a customs union - Labour's key demand in the talks.
They argue, such a proposal would mean Northern Ireland being treated differently to the rest of the United Kingdom and remaining in a customs union with the EU indefinitely.
It would be followed by negotiations on a new trade deal with the EU.
DUP Westminster leader Nigel Dodds said: "If the prime minister brings the withdrawal bill to the Commons for a vote, the question will be, 'What has changed?'".