The Equalities and Human Rights Commission (EHRC) launched an investigation in May into whether the party has unlawfully discriminated against or victimised Jewish people. The results will be published by the end of this year or early 2020. But MPs will try to oust Mr Corbyn if the report finds Labour institutionally anti-Semitic.
One MP told the Huffington Post: “It is unbelievably shameful that the Labour Party is being investigated by the EHRC, so if they find against the Labour Party, Jeremy Corbyn as leader has to take responsibility for that and stand down.
“But if he doesn’t stand down, what hope is there left that this racism in our party will ever be addressed?
“A challenge to his leadership will become inevitable.”
Another MP added: “It is a growing view that MPs will have to table a no-confidence motion.
“If Labour is said to be anti-Semitic by the Equality and Human Rights Commission – an organisation which was set up by a Labour government – and therefore racist, the leader should resign.
“If he doesn’t resign, there will be a clamour for a vote of no-confidence.”
A vote of no confidence can be triggered if 20 percent of MPs, which makes up 49 of them, nominate an alternative leader.
Labour has denied Mr Corbyn or the party is anti-Semitic and has said complaints are properly dealt with.
The party has faced a huge amount of backlash over recent weeks.
Last week, a BBC Panorama documentary aired interviews with former staff members about anti-Semitism within the party.
The programme claimed that senior figures, including Mr Corbyn’s communications chief Seumas Milne and general secretary Jennie Formby, had interfered in anti-Semitism investigations – claims the party deny.
Most recently, Shadow Brexit minister Dianne Hayter was sacked after she compared Mr Corbyn’s leadership to “the last days of Hitler”.
She said the party refused to share information with the National Executive Committee, including party finances, membership figures and the anti-Semitism data shared with the Equality and Human Rights Commission investigation.
Ms Hayter said: “That declaiming of intelligence, the refusal to share is an absolute symbol of the bunker mentality.
“Those of you who haven’t read the book will have seen the film ‘Bunker’, about the last days of Hitler, where you stop receiving any information into the inner group which suggests that things are not going the way you want.
“That seems to be where we are at the moment: having the leadership in a bunker so they are not hearing in those views, that evidence, that is in conflict with what they are trying to do, to the extent that even undermines what they are trying to do.”
But a Labour spokesman told HuffPost UK: “Diane Hayter has been sacked from the frontbench position with immediate effect for her deeply offensive remarks about Jeremy Corbyn and his office.
“To compare the Labour leader and the Labour Party staff working to elect a Labour government to the Nazi regime is truly contemptible, and grossly insensitive to Jewish staff in particular.”