The party is braced for the findings of a major documentary investigation into its handling of anti-Semitism claims and the shadow cabinet is also divided over Brexit and whether Labour should campaign to stay in the European Union in another referendum.
Labour's 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 BBC Panorama documentary, which is due to be aired on Wednesday.
According to the paper, Carter Ruck - acting on behalf of Labour - has written to Sam Matthews, the party's former head of disputes, 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 a further sign of unrest, the Sunday Times reported that two of Mr Corbyn's closet allies in the shadow cabinet, John McDonnell and Diane Abbott, have called on Mr Corbyn to sack key members of his inner circle - chief of staff Karie Murphy and communications and strategy chief Seumas Milne.
Mr McDonnell rejected the claims, insisting he had not called for anyone to be sacked.
He told the BBC'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."
In an effort to play down the row, shadow cabinet minister Barry Gardiner said: "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 also 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 BBC documentary, entitled Is Labour Anti-Semitic?, will see reporter John Ware explore the ongoing anti-Semitism row, and will feature interviews from "key insiders", according to the programme synopsis.
A spokesman for the show 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."
The party is also struggling to reach a united policy on Brexit, with Mr Corbyn expected to have further consultations with trade union bosses about Labour's stance on another referendum.
In March, Mr Gardiner had said that Labour is "not a Remain party now", but he told Sky News: "We have always been a remain and reform party. We tried to reconcile ourselves with what the democratic will of the people was at that referendum and we tried to do that sincerely.
"We now have two Conservative putative prime ministers who are saying they are happy to take us out on a no deal."
Mr McDonell said Labour had to decide on its Brexit policy "sooner rather than later", adding that he would vote to stay in the EU in another referendum and "would want to campaign for Remain".