Sky News understands Mrs May would struggle to delay the vote because the debate leading up to it has already started - meaning she would need to win another vote adding an amendment to push it back.
In the Commons, MPs have continued their debate on the Prime Minister's deal, with critic after critic on all sides standing up to say why they don't want to back it.
She suggested MPs could be "given a role" in deciding whether to activate the backstop, which is created to stop the return of a physical border.
Britain's Prime Minister Theresa May speaks during the scheduled Prime Minister's Questions time in the House of Commons, in London, December 5, 2018.
The government had refused previous requests to publish the advice, which comes just a week before MPs vote on the deal itself, saying it would set a risky precedent if the Attorney General could not provide the Prime Minister with honest, confidential legal advice without fear of it being made public.
She said: "I am talking to colleagues about how we can look at parliament having a role in going into that and coming out of that".
The Times newspaper reported that senior ministers were urging May to delay the vote for fear of a rout and several lawmakers said they suspected the government may try something to postpone what would be a game-changing defeat.
In an interesting aside, Stephens noted that it is unlikely that Cox himself would have actually written the advice; it would be usual for an attorney-general to seek advice from a legal expert in that field.
'The most important thing is to have clarity about how we might remove ourselves from a backstop, ' Sir Graham told the BBC's Newsnight.
It is likely to be seized upon by Tory critics of Mrs May's deal, who argue that the backstop arrangement to keep the Irish border open will deny the United Kingdom the power to withdraw from a customs union without agreement from Brussels.
On Tuesday night, Mrs May had made a last-ditch attempt to rally MPs behind her Brexit deal after suffering the historic humiliation of seeing her Government found in contempt of Parliament.
"I've been speaking to factory workers in Scotland, farmers in Wales and people right across the country, answering their questions about the deal and our future".
"The alternative is uncertainty and risk - the risk Brexit could be stopped, the risk we could crash out with no deal".
Bob has previously said he will support the Prime Minister's deal to secure Brexit.
May hinted she might give parliament a greater role in deciding whether to start the backstop or extend a transition period under which more European Union membership terms would apply.
It comes after Mrs May delivered her opening address on Tuesday, a week before MPs are set vote on whether to pass her deal on December 11. Another said it was: "Too little, too late".