He also said ministers were determined the United Kingdom should have an independent trade policy outside the EU - adding this ruled out any suggestion of remaining in the customs union.
"There has to be a discussion about the options that we put forward and we've put forward the three options that I've outlined".
"I propose we negotiate with Europe to extend Article 50 for one year not as a delaying tactic but for a goal; that we agree, and the European Union accepts, a unique democratic innovation - the convening of nationwide citizens' assemblies".
However, the Labour leader stressed the party would still prioritise trying to secure a general election or achieve a Brexit deal on the terms they have demanded.
"My door remains open to a meeting without preconditions", she said, adding that she would be "happy to discuss" Corbyn's proposals which include a customs union with the EU.
Sight of the document comes just days the prime minister's Brexit deal suffered a historic defeat in Parliament.
Against the prime minister's deal, Remain led by 65% to 35%, while against no-deal was 59%-41% in favour of staying in the EU.
But opposition Labour leader Jeremy Corbyn said he would only meet May if she could "remove clearly, once and for all the prospect of the catastrophe of a no-deal Brexit".
Labour lawmaker Ben Bradshaw accused May of being "in a total state of denial" about how radically her Brexit plan needed to change. "Child poverty has risen by over half a million since 2010 and there are now four million working people living in poverty", she said.
Brexit protesters demonstrate by the houses of Parliament in London.
European leaders are now preparing for the worst, although German Chancellor Angela Merkel said there was still time for further talks.
He told her that "the starting point for any talks about breaking the Brexit deadlock must be that the threat of disastrous no-deal outcome is ruled out".
Companies warned of catastrophic job losses and chaos at ports if there was no deal.
In his letter to MPs Mr Corbyn thanked them for their support in the debates against Mrs May's Withdrawal Agreement and then in the defeated no confidence vote on Wednesday.
Mitsubishi UFJ Financial Group Inc. has gained securities business approval in the Netherlands, while Mizuho Financial Group Inc. has done the same in Germany.
May's deal was doomed by deep opposition from both sides of the divide over the U.K.'s place in Europe.
Accusing Leave campaigners of misleading voters about the kind of Brexit they could obtain, Mr Macron said: "Good luck to the representatives of the nation who has to implement a thing which doesn't exist and has to explain to the people: you have voted on a thing, we lied to you". Assurances from European Union leaders that the backstop is intended as a temporary measure of last resort failed to win over many British lawmakers.
"Maybe we'll make improvements on one or two things, but I don't really think so because we've reached the maximum of what we could do with the deal", the French leader said.
Varadkar said if May's government was willing to shift some of its "red lines" in negotiations - such as leaving the customs union and EU single market - then the position of EU negotiators would also change.