Party leader Jeremy Corbyn, who has seen virtually the whole of his front bench team resigning from his shadow cabinet, has offered a peace formula to his estranged party colleagues.
"She has the signatures", one source said, referring to the number of nominations from Labour MPs and MEPs needed to mount a challenge under party rules.
It comes after Labour officials revealed 60,000 new members have joined the party over the last week to head off a plot to try and remove him from office amid a challenge from Angela Eagle.
The event is being organised by the Teesside branch of Momentum - the successor of the Jeremy Corbyn for Labour Leader campaign.
He said it was up to the thousands of Labour members to decide on any change of leader and that "we should all respect the constitution of the party".
But People's Momentum, the hard-Left grassroots movement which backs Corbyn, has recruited numerous 60,000 new members who have flocked to join the party in the last week.
Scottish Labour's deputy leader admits his party looks "even weaker and more divided" than the Tories following the Brexit vote.
"They don't have a candidate who can beat Jeremy Corbyn", he added.
Angela Eagle says she has support to "resolve this impasse" over the Labour Party leadership "if Jeremy doesn't take action soon". Unions supply much of the membership and a lot of the funding on which the Labour Party relies.
However, Mr McCluskey said it was "unhelpful" for ex-Labour leaders who had lost previous elections to be "dragged out to be part of an unedifying coup".
"Jeremy Corbyn has shown incredible steel in staying there and not falling, and staying there on behalf of the principle of democracy in the party".
Ms Eagle, who was expected to launch her bid for the top job last week, warned that the threat of a contest had not gone away.
Allies of Mr Watson have been urging him to stand but so have supporters of Owen Smith, who quit as shadow work and pensions secretary last week.
"I think he will win, but you can never predict these things, it's a democratic election" he said.
On 2 July, Corbyn was reportedly held back by aides at an anti-racism rally in north London after a reporter asked him if he was "running away" from answering questions on his leadership.
Speakers highlighted Jeremys history of standing together with them on picket lines about issues that were important to them and said "now we must stand with him".
Middlesbrough Labour councillor Jordan Blyth added: "I believe that 172 MPs should not be able to overturn the will of hundreds of thousands of party members".