If Corbyn remains on the ballot, he will probably win, plunging the party into a crisis that could see most of its MPs splitting off into a separate group, possibly leading to a permanent tear in the party.
Corbyn, despite a huge revolt by the majority of his MPs and losing a confidence vote, has refused to resign, promising to fight any leadership challenge.
With the Conservative Party also in turmoil following the Brexit vote, British media have begun to speculate that Conservative and Labour MPs who are pro-European could create a new centrist party as the traditional parties move further to the right and left.
This meant that 81% of MPs voted against their leader.
It is unclear yet whether any other candidates will put themselves forward for the position.
In what her supporters were touting as a major speech, the former shadow business secretary will seek to present herself as a potential boss of a credible opposition party which voters could trust to run the country.
"I'm expecting to be on the ballot paper", Corbyn told BBC television.
Among the many issues roiling the Labour party is the question of whether the incumbent leader is automatically entitled to be on the ballot in the case of a leadership challenge.
Ms Eagle is facing a vote of no confidence by members of her local party, which backs Mr Corbyn's leadership.
But she added: "Anyone who aspires to lead the parliamentary party who can not get 51 members, 20% of the parliamentary party, to back them is not going to be able to do the job properly".
Asked about Eagle's challenge, Corbyn said: "I'm disappointed, but obviously she is free to do that if she wishes to".
However, Labour MP Kate Green backed up Mr Smith, saying: "I was in that meeting, John".
Only this can account for the depiction of Corbyn, who has offered up only the mildest of reformist measures, as the representative of a revolutionary insurgency against Labour's "traditional" values.
Ms Shabi asked: "I am wondering why this time round... given the sort of political record you have got, supporting the Iraq War, opposing the inquiry into the Iraq War, supporting university tuition fees, abstaining from the welfare bill..."
"We have worked together in the past nine months in the shadow cabinet and this is an opportunity when we could be putting enormous pressure on this Tory government".
Now the country's opposition Labour Party - which should have been in good position to capitalize on the chaos inside the ruling Conservatives - has also made a decision to tear itself apart as the fallout from last month's stunning referendum vote in favour of a Brexit continues to spread.
The party's National Executive Committee will decide on the rules after a contest is formally triggered.
During her interview, Ms Eagle described herself as a "good, sensible, down-to-earth woman with Northern roots".
"If you fail, you can't take the party down with you - that's not fair".