The legislation is a requirement from the Supreme Court, which said that May needs lawmakers' approval to be able to invoke Article 50 of the EU's Lisbon Treaty, the formal procedure for leaving the bloc.
The House of Commons will discuss changes to the bill made by the House of Lords, particularly for granting permanent residency rights to EU nationals living in Britain and giving parliament a final say on Brexit.
But some Conservative MPs could vote in favour.
The amendments are expected by commentators to be voted down, meaning the bill would go back to the House of Lords for final approval and then to Queen Elizabeth II for her assent.
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Keir Starmer, the main opposition Labour Party's chief Brexit spokesman, told parliament that May was planning to invoke Article 50 on Wednesday or Thursday.
The government has only said that she plans to do so by the end of March, after which the EU has said it will respond with its strategy within 48 hours.
But he added: "If you don't know where you are going to end up you can't have a transitional arrangement".
Davis said his aim was not to "divide and conquer" other EU member states but to have a strong and stable European Union as a future key trade partner.
He confirmed, however, that Britain would "not be able to remain in the customs union as it currently stands" so as to strike free-trade deals with other countries.