"I would ask her to think for a moment", he said. I'm a woman from the working class North - I understand metropolitan things too, ' she added.
The leadership move against Mr Corbyn comes as the party faces bitter legal wrangles over how the election will be organised.
Mr McDonnell responded by saying the claims he was prepared to split the party were "complete rubbish".
Mr Corbyn will press ahead with a planned speech to the policy conference of Unite in Brighton on Tuesday as sources said he has been told he can not attend the NEC meeting.
"This country has voted to leave the European Union with people now facing vast insecurity and a rising tide of xenophobia and racism we need Angela as leader with her sights set firmly on bringing the party together and leading a coherent and determined Opposition which will be a credible party of government".
Labour's leadership battle looks more likely to end up in the courts with rebels and Jeremy Corbyn loyalists rowing over whether the leader should be able to stand in the contest automatically. "If she runs, party members will be offered a clear political choice".
But Mr Corbyn's backers say that as leader, he has an automatic right to stand, especially as he won 59% of the membership vote last September.
"I am not contemplating losing this contest, I am in it because I want to win it for the best interests of a strong Labour Party", Eagle told ITV.
Mr Corbyn has said however, that he will not "betray" the thousands of party members who elected him as leader a year ago.
An election to challenge Jeremy Corbyn for the leadership of the Labour party has been officially triggered, the party has said. Thousands of new members have joined, with many believed to back him. "This isn't about splitting the Labour Party, it's about creating a strong, united party". Well, if so, then our members ... that's democracy'. "I have launched my campaign - I intend to win". However, the fee will be set by the NEC and they may decide to change it, given the volume of people who signed up last time. But I still think he should be allowed onto the...
- Corbyn on the ballot?
Former Shadow Cabinet Minister Angela Eagle launches her bid for the Labour leadership at a press conference at Savoy Place on July 11, 2016 in London.
"It is time for the Labour Party to unite and ensure the millions of people in the country left behind by the Tories' failed economic policies, have the opportunity to elect a Labour government".