Theresa May should call a fresh general election if she can not get agreement on her Brexit plan, Jeremy Corbyn said.
He said it is conceivable there is "no majority in Parliament for any Brexit deal" and if this was the case then the party has to look at all options.
He said: "I would urge everybody within the Labour Party to listen to the voices that have come out in recent days and get to a position where we are supporting the full definition".
Asked if the Tories were splitting, Mr Rees-Mogg said: "I think there is one issue of grave concern and that is the Government has been briefing Labour members of Parliament".
"Here we are, two years since the referendum and the Government still hasn't produced a white paper on its own negotiating stance".
"And so you keep your options open".
Sir Keir also told the programme Labour wanted a customs union that "does the work of the customs union".
"We will obviously examine the details of this alleged agreement within the Cabinet".
He said: "It is Parliament that should decide what happens next, it should have the power to decide the options, and this might involve a general election or a "People's Vote". According to rumors, Conservative member of parliament (MPs) have reached the magic number of 48 letters required to force a confidence vote, which could put the United Kingdom in the hands of a new government and a new approach to Brexit.
He added: "We're not calling for it. It's time for the Labour party to give up the idea of a second referendum".
He said the UK's best interests and the best economic interests are "not the same thing" and the referendum result had to be respected.
The Unite union, Labour's biggest financial backer, is also open to the possibility of a second referendum if the Brexit deal is unacceptable.