John McDonnell and Michael Meacher insist they will be able to mount a left-wing challenge to Gordon Brown.
However, they will not confirm that one of them has sufficient support from MPs to make it onto the leadership ballot until Monday.
In order to make it onto the ballot papers, a candidate for the leadership must have the support of at least 44 other Labour MPs - equal to an eighth of the parliamentary Labour party.
Both candidates announced their intention to challenge Mr Brown but were repeatedly warned they were unlikely to receive the necessary support to mount a serious challenge.
To avoid splitting the left-wing vote, Mr Meacher and Mr McDonnell announced last month that only the candidate with the most support from MPs would officially seek nomination.
The pair met today to compare backing and claim it is "too close to call". They will spend the weekend canvassing support before reaching an agreement on Monday.
The cancellation of today's press conference had caused some to write-off the prospect of a leadership contest. However, a spokesman from the Meacher campaign said the two candidates had not known until today what backing the other had and were still negotiating who was the strongest candidate.
He insisted that by combining support one hopeful would have the necessary 45 signatures needed to stand. Asked whether they could be certain MPs would transfer their backing between the two, he replied they were "confident".
Speaking to the BBC, Mr McDonnell insisted he and Mr Meacher had the numbers to stand between them.
He dismissed claims that neither presents a credible challenge to the chancellor.
"Anything can happen," Mr McDonnell argued. "No one had ever heard of David Cameron before the [Conservative] leadership election."
Mr McDonnell has rejected the suggestion he is launching a 'kamikaze campaign' simply designed to force Mr Brown into a contest.
Announcing his intention to stand, he said he was not a "stalking horse" candidate, but a serious challenger for the leadership.
Writing in the Guardian he said: "Some have argued that instead of an open democratic election for the leader of the party, there should be a smooth transition or virtual coronation of his successor.
"This would deny party members the opportunity of openly debating the issues facing our party and the future direction of the country. An election for the leader of the party will allow for a democratic debate on the future of Labour."
Mr Meacher argues the Labour party needs to consider a change of direction, pointing out the government has lost four million votes since 1997.
He said: "New Labour and Tory policies have become distinctly similar, almost overlapping, which means that politics has become increasingly fixated on personalities, as though a blanket consensus on policy has been achieved.
"It's time, not for a return to Old Labour, but for the advance of mainstream Labour - which represents the majority opinion - that has been suppressed for over a decade."
However, with 200 MPs already announcing their support for Mr Brown, it is doubtful anyone other than the chancellor will take over as prime minister when Mr Blair steps down on June 27th.
In an indicative verbal slip, the speaker of the House of Commons today referred to Mr Brown as the 'prime minister'.
A YouGov poll of party members last month also found 80 per cent back Mr Brown. Mr McDonnell polled just nine per cent and Mr Meacher six per cent. At the time, Charles Clarke was still considered a possible candidate, but received support from just five per cent of party members.
The deputy leadership contest is set to be far more open, with six stated candidates and no clear winner. Hilary Benn, Hazel Blears, John Cruddas, Peter Hain, Harriet Harman and Alan Johnson all hope to replace John Prescott as deputy leader.