The BBC’s political correspondent Ellie Price said she had been told by Labour’s National Executive Committee that there were no plans to change existing rules but many MPs on the right of the party remain concerned.
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“There is no way that we will allow MPs to be deselected in that way”, McDonnell said.
But he went on: “If you have a thousand new members joining your party because they supported Jeremy Corbyn’s policies and you have an MP completely undermining him… they should have the right to challenge that”.
Veteran MP Frank Field warned any such move could be met by a mass rebellion, with Labour MPs backing their ousted colleagues in by-elections in defiance of party rules.
It has been claimed that left-wing activists are flooding the constituency parties of centrist MPs, including Chuka Umunna and Harriet Harman, with a view to unseating them when Boundary Commission changes kick in.
It comes after campaigning Rochdale MP Simon Danczuk said he was prepared to run against Mr Corbyn as a stalking horse candidate.
Sources close to Mr Corbyn said the allegations were without foundation.
He argued that “huge numbers” of parliamentarians should be ready to campaign against the official Labour candidate on grounds that “they can’t expel huge tranches of Labour MPs”. “We are not in favour of reselection of these MPs”, he told BBC1’s Andrew Marr Show.
Mr Danczuk told The Sun: “This is a totally freakish appointment of a man more likely to become the story rather than control our party’s message”.
If you’ve had a doubling of the Labour party membership because people see there’s a real chance of change, and if Jeremy Corbyn looks like he is doing a good job, you wouldn’t expect… if people say “every day I see my MP undermining the Labour leadership, opposing the policies we came into politics for”.
‘What I would say to those members that are anxious is work now getting to know all the new members.
He added: “We finally have Tory MPs squirming over the vote on tax credit cuts and we unleash more process barminess to divert attention”.
But the appointment was described by MP Simon Danczuk as “totally bizarre” and leading Blairite John Woodcock said voters “deserved better” in an online condemnation of the announcement.
“So this week we launch an organisation called Labour Together”.
“The country needs a Labour party capable of boldness, but absolutely clear that what matters is building a broad coalition of electoral support”.
“Jeremy Corbyn has rightly challenged the party to rethink the way in which it does politics. They have a right to defend themselves from the occupier”.
Critics of the appointment have pointed to a 2013 article in which Mr Milne suggested that the murder of Fusilier Lee Rigby “wasn’t terrorism in the normal sense of an indiscriminate attack on civilians” because the soldier had served in Afghanistan.
“There will be a large group I would hope in Parliament of MPs who will, if colleagues are unfairly treated, encourage their colleagues to stand in by-elections, to stand as independent candidates and a large number of us including myself, would go and actually campaign for them”.
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“And now think it is probably in everyone’s interests that I turn my phone off for the evening”.
