It came as deputy leader Tom Watson hit out at a clampdown on former staff blowing the whistle on its handling of anti-Semitism allegations ahead of the new documentary.
The Sunday Times reported that two of Mr Corbyn’s closest allies in the shadow cabinet, John McDonnell and Diane Abbott, called on Mr Corbyn to sack two members of his inner circle – gatekeeper Karie Murphy and communications and strategy chief Seumas Milne.
The pair reportedly warned Mr Corbyn that, unless he stops listening to the two aides and backs a new referendum on Brexit, his leadership would be untenable.
However Mr McDonnell today dismissed reports of a rift and insisted he had not called for anyone to be sacked.
He told BBC1’s Andrew Marr Show: “I have confidence in them, of course I do. I have not told anyone to be sacked or anything like that, this is all myth.
“But let’s make it clear, Jeremy and I talk about policies on a daily basis. Yes, we will disagree on things but we will then come to an agreement.”
He blamed the story on journalists attending summer receptions and “drinking some of the most nauseating wine ever produced from a grape”.
The Sunday Times also said up to half a dozen ex-employees have torn up non-disclosure agreements (NDAs) to speak to a BBC Panorama documentary about anti-Semitism.
According to the paper, law firm Carter Ruck has written to Sam Matthews, the party’s former head of disputes, on behalf of Labour warning he could face legal action for breaking his NDA.
A letter is reported to warn that the party “cannot be expected to and will not tolerate its former employees wantonly disregarding their obligations by selectively leaking information to the media”.
Another former aide also received warnings last year from a different law firm representing Labour, the paper said.
Mr Watson said: “Using expensive media lawyers in attempt to silence staff members is as futile as it is stupid.
“It’s not the Labour way and I deplore it.”
In response to the row, shadow cabinet minister Barry Gardiner told Sky News’s Sophy Ridge On Sunday: “The idea that they put forward that there’s a civil war in the Labour Party – let’s look at the real divide in this country.
“The real divide in this country is not within the Labour Party, the real divide in this country is between what the Conservatives are trying to do with our country and the rest.”
He defended the party’s use of gagging clauses, insisting they were not being used to cover up wrongdoing.
The shadow international trade secretary said: “We absolutely do not use gagging orders to hide anything that is illegal or improper.
“We use gagging orders only to stop former members of staff from leaking confidential information where we have an obligation to protect individuals and for doing that in a party political or partisan way for political purposes.”
He said he would welcome “any objective, impartial investigation that’s going to help us to get rid of anti-Semitism in the Labour Party” but “my understanding of this programme is that has not been balanced and impartial in that way”.
It involved talking to former party staff members who had a “political axe to grind”, he claimed.
The documentary Is Labour Anti-Semitic?, due to be aired on Wednesday, will see reporter John Ware explore the ongoing anti-Semitism row, and will feature interviews from “key insiders”, according to the programme synopsis.
A Labour source accused the BBC of creating a “one-sided narrative” and said it would be complaining to the director-general, telling the Sunday Times: “With a possible general election around the corner, this smacks of bias and interference in the political process by the BBC and a clear breach of their own editorial guidelines.”
However a spokesman for Panorama said: “The Labour Party is criticising a programme they have not seen.
“We are confident the programme will adhere to the BBC’s editorial guidelines.
“In line with those, the Labour Party has been given the opportunity to respond to the allegations.”
Wes Streeting, Labour’s MP for Ilford North, said he would “whistleblow in (the) House of Commons for anyone who needs me to do so”.
Writing on Twitter, he said: “Labour opposes NDAs yet seems to impose them. I’m protected by Parliamentary privilege. I’ll whistleblow in House of Commons for anyone who needs me to do so. Sunlight is the best disinfectant. No more excuses or hiding places. You should promise the same @jeremycorbyn.”
Chairman of the Jewish Labour Movement Mike Katz said: “Given Labour has called for scrapping of NDAs & greater legal protection for whistleblowers, it’s both hypocritical and just plain wrong of it to set expensive lawyers on former staff who are acting in the public interest to shine a light on institutional anti-Jewish racism.”