UK Prime Minister Boris Johnson said earlier that he would not put forward a nominee.
In spite of the uncertainty, whatever the decision, it will be taken by written procedure. The text said London could leave the community earlier if parliament ratified the text of the exit agreement.
The "flextension" is seen as a compromise.
The ex-Labour leader said: "The sensible thing for him [Jeremy Corbyn] to say to Boris Johnson is, "Yes, I'll agree to your general election, but you've got to agree to timetable proper scrutiny of your bill and allow us to amend that so that we rule out no deal as the outcome of the future negotiation".
It's the second time the Brexit deadline has been changed since British voters in 2016 referendum made a decision to leave the bloc.
It comes as France had been insisting on "justification" for a Brexit extension and as British MPs prepare to vote this afternoon on holding a general election.
It will be his third attempt at getting support for the United Kingdom to go to the polls.
But the chances of enough MPs backing the motion - which requires the support of two-thirds of the House of Commons - appear uncertain, with Labour not committing to how it plans to vote.
He has said for months that the United Kingdom will leave the European Union on October 31 "come what may" - with a Brexit deal or without one. He said the only way to break the country's political logjam was to call a new election and get rid of what he called the current "zombie Parliament". Johnson is obliged by legislation passed by parliament last month to accept an extension once offered.
"We need a new parliament by Christmas so we can get Brexit done in January and the country can move on".
Tony Blair has urged Labour to ensure a no-deal Brexit is ruled out completely - including if upcoming European Union trade talks turn "ugly" - before agreeing to an election.
Brexit has increasingly dominated politics, pushing other pressing issues aside.
If that initiative flops, the SNP will table a vote of no confidence in Johnson under the Fixed Term Parliament Act on Tuesday, with a view to compressing the 14-day schedule before the consequential second vote to just one or two days.
"The conditions of the extension have been specified and reinforced, notably on the fact the deal is not renegotiable", a French diplomatic source told AFP in Paris. A vote is due in parliament later on Monday.
He says, "It's time to give the British public the final say on Brexit".
A decision had originally been expected today.
A further reason that has been suggested for both main parties' stances is that the ruling Conservatives have been consistently ahead of Labour in recent opinion polls.