And speaking on the fringes of the Labour conference on Sunday evening, Mark Serwotka, the general secretary of the PCS union, also said there should be "no second referendum on the principle" of EU membership.
The Daily Express runs with the headline: "Outcry at Labour's betrayal of Brexit", and says the Labour leader faced a "furious backlash" after confirming he was ready to join calls for a re-run of the 2016 poll if delegates back the demand in a vote at the party's conference. In fact, many members suspect another artfully constructed compromise is in the offing.
Labour is expected to discuss several motions on Brexit at its conference, and it remains unclear what the proposal on a second referendum might be - it could be a clear backing of a vote or something less black-and-white.
Shadow chancellor John McDonnell has already said he would like Labour's next leader to be a woman but Ms Nandy said the party should go further and consider a joint male-female leadership team as the Green Party has previously had.
Mr Corbyn told an eve-of-conference rally in Liverpool: "If this Government can't deliver, then I say to Theresa May: the best way to settle this is to have a general election".
"Of course we're a democratic party, but before we get that we want a general election, because this government has made a complete fist of Brexit, they haven't been able to negotiate a deal", he said.
"What comes out of conference I will adhere to".
The Conservatives seized on Labour's potential support for a people's vote, with the prime minister tweeting that the party wanted to "take Britain back to square one - betraying all those who voted in the 2016 European Union referendum".
For those pressing for a second referendum, or a People's Vote, the motion was little more than a fudge.More news: Russian Federation to supply S-300 air defense system to Syria
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There was a similar message from deputy Labour leader Tom Watson, who told The Observer: "Jeremy and I were elected in 2015 to give the Labour Party back to its members".
The YouGov survey of more than 1,000 Labour members found 86% support a referendum on the outcome of Brexit talks, against just 8% who oppose it.
And it is a party which seems to have a renewed confidence after winning a greater vote share than expected in an election previous year.
BBC political correspondent Iain Watson said the final wording of any motion would be crucial and that Mr Corbyn would be hoping it did not tie his hands - but that some members would be pushing for a clear commitment to a new referendum.
Some 81% believe their standard of living would get worse after Brexit and 89% said it would be bad for jobs.
The overhaul of party rules come after several Labour moderate MPs have faced no confidence votes from their local parties after they spoke out against Mr Corbyn's over anti-Semitism.
He told the Today programme: 'The next leader of the Labour party has to be a woman'.
"There were 300 people in the room and that was absolutely clear", he said.
Labour leader Jeremy Corbyn accepted he would be "bound" by the outcome of Tuesday's conference motion. "We desperately need a general election".