Lawmakers in the lower House of Commons have already given their go-ahead to the so-called Brexit Bill, which gives May the authority to invoke Article 50 of the Lisbon Treaty to formally initiate Brexit negotiations.
The UK government does not have a majority in the House of Lords, where as many as 190 peers are due to speak during the debate, which will include a number of amendments being proposed.
The voting in the upper house of Parliament, whose total strength is in excess of 700, is expected by tomorrow evening.
The Lords begins the Second Reading debate on the Bill on Monday and a vote will take place on Tuesday only if peers allow government legislation through unopposed at this stage.
More From This Section
Detailed scrutiny of the bill at committee stage is due to take place on February 27 and March 1.
If the bill is not amended, then it could theoretically be approved by the Lords at Third Reading on March 7 and go on to become law.
Parliamentary norm would lead to MPs then overturning any Lords amendments.
The Conservatives have the largest number of peers in the Lords, with 252 members, but the Opposition has 202 Labour peers and 102 Lib Dems, who are expected to join forces against the government.
It will be the 178 crossbench in the Lords, who are not aligned to any party, who are expected to determine the final outcome of the Second Reading.
May has declared her intention to invoke Article 50 by the end of next month and believes she can stick to that timetable.