The government’s Brexit strategy will come under scrutiny when an official policy document setting out its plans is published later.
The White Paper, which was promised after pressure from MPs, comes after the Commons voted to allow the PM to begin the Brexit process.
MPs backed the European Union Bill by 498 votes to 114 on Wednesday night, with 47 Labour rebels voting against.
The bill will now face more debate before it can become law.
MPs will discuss the bill in more detail next week when it reaches the committee stage in the Commons, and Labour has vowed to force through amendments.
Hundreds of amendments have already been tabled for debate between Monday and Wednesday, with objectives set out in the government’s strategy expected to attract more.
Shadow cabinet members Rachael Maskell and Dawn Butler quit the party’s front bench shortly before Wednesday evening’s vote, and in total, 13 Labour frontbenchers voted against their own party position which was to support the bill.
Speaking on BBC Radio 4’s Today programme, shadow chancellor John McDonnell said other parties had also been divided on the issue, with two of the Liberal Democrats’ nine MPs abstaining despite orders to back the bill.
Mr McDonnell said a decision on whether frontbench rebels could remain in their jobs would be taken “in due course”, and that the atmosphere in his party was “one of mutual respect”, with determination to oppose a “reckless Brexit”.
He said Labour “may look divided” but would unite after the government triggers official negotiations under Article 50 of the Lisbon Treaty while “the Tory Party will split apart”.
The Brexit bill was published last week, after the Supreme Court decided MPs and peers must have a say before Article 50 could be triggered.
It rejected the government’s argument that Mrs May had sufficient powers to trigger Brexit without consulting Parliament.
Iain Watson, BBC political correspondent, said a “sizeable” Labour rebellion could grow further if amendments were not passed.
In truth, the substance of the government’s white paper will be similar to the speech the prime minister gave last month, setting out her priorities for the forthcoming negotiations with the EU.
Only one Conservative MP – the former Chancellor Ken Clarke – voted against the principle of leaving the EU last night but some of his colleagues are more likely to defy their government on the detail.
Three shadow cabinet members refused to support triggering Article 50 and stepped down before the vote.
Jeremy Corbyn is yet to decide whether to discipline the 10 junior shadow ministers who rebelled, or indeed the three whips who were supposed to impose party discipline rather than flout it.
With the possibility of two more shadow cabinet members going next week, Mr Corbyn will have to decide whether to relax his instruction not to block Brexit if Labour’s amendments are defeated.
The SNP, Plaid Cymru and the Liberal Democrats all opposed the government’s bill, alongside Tory Ken Clarke.
The SNP’s foreign affairs spokesman at Westminster, Alex Salmond, said there would be “detailed questions” about the bill during its next stage.
He said “the calibre of the government will be judged by how they respond to the amendments”.
Mr Clarke, the only Conservative MP to defy his party by voting against the bill, said the result was “historic”, but the “mood could change” when the “real action” of negotiations with the EU starts.
Mrs May has set a deadline of 31 March for invoking Article 50.
Talks with the EU are expected to last up to two years, with the UK predicted to leave the 28-member organisation in 2019.
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