Mr Corbyn described Mrs May's offer to talk to other party leaders as a "stunt" but said he was "quite happy to talk to her" if the "threat of a no-deal outcome" is ruled out.
The comments come after a YouGov poll claimed the Conservative Party were still more popular than Labour.
In a live television address late on Wednesday evening, Mrs May said talks had been constructive, adding: "I am disappointed that the leader of the Labour Party has not so far chosen to take part, but our door remains open".
May, who narrowly defeated a no-confidence vote in her Conservative government triggered by Corbyn this week, said it was "not within the government's power to rule out no-deal" because by law Britain will leave the European Union without an agreement on March 29 unless Parliament approves a deal before then.
"Prime minister, take it off the table and have a serious discussion about how we approach the future", he said, warning May against any attempt "to blackmail MPs to vote through her botched deal on a second attempt".
One of its architects, Cathleen Clarke, 22, said had been "inspired" by Mr Corbyn when he first ran for the Labour leadership.
Mrs May has already met party leaders who openly want to stop Brexit - Sir Vince Cable and Ian Blackford - so any meeting of minds with them is unlikely.
"The government confirmed that she would not take "no-deal" off the table", Corbyn said in a speech in Hastings, scene of a battle in 1066 that ushered in the Norman conquest of England.
The man who was happy for talks with a rogue state breaching worldwide norms of decent behaviour and being shown to be blatant liars has angrily turned down the opportunity of talking to Theresa May as she tries to plot a pathway for the United Kingdom out of the Brexit mess.
The €50m will be invested in infrastructure at ports, airports and borders "most concerned" by the prospects of a no-deal, he said.
"I believe other parties are taking the same view", the Lib Dem leader said. "She still thinks it's going to be possible to tweak this deal sufficiently to get the MPs that voted against it to swing behind it - I remain pretty sceptical about that".
Amendments are expected to be tabled to seek parliamentary support for a range of options, from ruling out no-deal to extending the two-year Article 50 process or calling a second referendum.
Mrs May is expected to maintain an intensive round of meetings and phone calls before setting out her Plan B on Monday, in a Commons motion which crucially can be amended by MPs.
He also suggested Article 50, the process taking the United Kingdom out of the European Union on 29 March, might have to be extended if an agreement could not be reached in time. Lawmakers would then have a chance to submit amendments before a full debate on January 29 - exactly two months before the Brexit date. An extension to Article 50 is inevitable now.
"If it instead backs some version of a Brexit deal which is worse than the deal we already have inside the European Union and would leave the country worse off, it risks losing millions of supporters and alienating a whole generation of young voters".