Mrs May earlier stressed the importance of next week's votes on the European Union (Withdrawal) Bill, which seeks to transfer EU law into United Kingdom law.
Brexit Secretary David Davis is reported to be threatening a Cabinet protest as top ministers are believed to have been banned from seeing it despite it reportedly being ready.
He said the detail of the document was still being discussed, adding: "It has been through one Cabinet committee, it is going to another one and it would be improper of me to pre-empt the negotiation there, but I suspect it will be fairly decisive tomorrow".
"Parliament should have the opportunity to debate and vote on it", he added.
Mr Corbyn said: "We are confident we can build a new relationship with the EU".
A struggle in May's team of ministers over future customs arrangements with the European Union has all but stalled Brexit negotiations, and there is little time left.
Meanwhile, Mrs May's decision to squeeze Commons consideration of the 15 Lords amendments to the EU Withdrawal Bill into a single 12-hour day on June 12 provoked an angry reaction on the opposition benches.
With Tory rebels set to side with Labour over measures aimed at keeping a customs union on the table, Mrs May engaged in crisis talks to avert a damaging defeat. "Why not just vote for the Lords amendment?"
Other contentious pieces of legislation - the Trade Bill and the Taxation (Cross-border) Trade Bill - will also return to the Commons before the summer.
He said: "The option of us continuing to participate in the single market is only dead insofar as the Labour frontbench seek to adopt that position and I sincerely hope that we will do right by our values and seek to keep us in the EEA".
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Mrs May also came under pressure from Tory MPs, with Crawley MP Henry Smith saying his constituents wanted her to get on with both Brexit and sorting out the rail mess.
"Labour will only accept a Brexit deal that delivers the benefits of the single market and protects jobs and living standards", Keir Starmer, Labour's Brexit policy chief, said on Tuesday.
With the support of Northern Ireland's Democratic Unionist Party (DUP), the government has a majority in the 650-seat House of Commons.
Tory support for the EEA has been signalled in an amendment to the Trade Bill.
Starmer said Labour was seeking a bespoke agreement "rather than a Norway-style deal", though it is unclear how Labour would negotiate earlier pledges on ending free movement of people, one of the four preconditions for staying in the single market.
He told BBC Radio 4's Today programme: "The difficulty with that, and I think everybody recognises this, is that there are very strong and very different views across the PLP on that particular amendment".
At an event hosted by the Open Britain campaign, he told the Press Association he would rebel on Tuesday to support the EEA amendment and a "large number" of Labour colleagues would do the same. But she did not say when.
If nothing else, however, the amendment puts the single market at the center of the debate, with Britain due to leave the European Union on March 29 and Prime Minister Theresa May struggling to unite her Conservative Party and government over a Brexit strategy.
"That has got to change, we can not allow this culture of fear that has developed to continue any longer".