But the government has insisted it would instead publish a reasoned statement, citing a need for Cabinet confidentiality.
Sir Keir also warned Labour would seek to call a motion of no confidence in the government if May loses a Commons vote on her Brexit deal.
Mrs May will also address the Commons as she tries to persuade MPs to support her Brexit deal in that vote on 11 December.
May has warned British lawmakers that if they reject the agreement, Britain could leave the European Union with no deal, a step which businesses fear could disrupt their supply chains.
Green Bay Packers fire coach Mike McCarthy
It was the first time Green Bay had lost to the Cardinals at home since 1949, when the Cardinals franchise was based in Chicago. Joe Philbin was named interim head coach, President and Chief Executive Officer Mark Murphy announced.
She said at a news conference that "passing this deal ... will take us to certainty for the future, and that failure to do that would only lead to uncertainty". A Northern Irish party which props up her minority government has said it will vote against it.
United Kingdom lawmakers are set to begin debating May's Brexit package this week, but the signs don't look promising for the prime minister.
The government says that if May's deal is voted down there is a risk Britain will exit the European Union with no agreement at all, with serious potential economic consequences.
The environment secretary warned a no deal Brexit would "cause hurt" and "turbulence".
Former foreign secretary Boris Johnson has already dismissed anxieties over a no-deal Brexit by comparing them to fears over the Millennium bug, while former Brexit secretary David Davis declared that "I don't find "no deal" intimidating at all".
Macron crisis escalating as Paris erupts in rioting
He then returned to Paris to view the Arc de Triomphe and hold emergency meetings with French ministers. He also met with police officers and firefighters who worked to contain the protests, BFMTV said .
While Labour has previously committed to following through on Brexit, support for a second referendum has been growing inside the party, and last month shadow chancellor John McDonnell said it was "inevitable" that if a general election was not possible "then the other option which we've kept on the table is a people's vote". "But it seems to me that if the prime minister has lost a vote of that sort of significance, then there has to be a question of confidence in the government".
A 27-page legal note prepared by the House of Commons EU legislation team reveals that if the United Kingdom entered the customs union backstop then its ability to strike new free trade agreements will be severely restricted.
"Get this wrong and we may put in peril the Brexit the British people voted for and want us to deliver". But on Monday Attorney General Geoffrey Cox, who wrote the advice, will offer only a limited summary of the government's legal position during a statement to parliament.
Labour sources said that Sir Keir was ready to sign a joint letter with the DUP's Westminster leader Nigel Dodds, Liberal Democrat Brexit spokesman Tom Brake and SNP Europe spokesman Stephen Gethins, asking Mr Bercow to allow a motion "that the Government has held Parliament in contempt".
Angela Merkel's plane makes emergency landing
German government planes, operated by the country's air force, have been plagued by technical problems in recent years. A senior journalist with the public national television ZDF said Merkel would spend Thursday night in Bonn.