The Labour leader is facing a no confidence vote over claims he fought a "lacklustre" campaign in the EU vote.
A Labour spokesman said Mr Corbyn had "lost confidence" in Mr Benn.
Shadow chancellor John McDonnell said Mr Corbyn "worked himself to the ground" during the referendum campaign.
Senior Labour sources also told the BBC that a significant number of shadow cabinet resignations were likely if Mr Corbyn were to ignore the result of the confidence vote.
Labour MPs Dame Margaret Hodge and Ann Coffey submitted a motion of no confidence against Mr Corbyn - who campaigned on the losing Remain side - in a letter to the Parliamentary Labour Party (PLP) chairman John Cryer on Friday.
The motion has no formal constitutional force but calls for a discussion at the next PLP meeting on Monday.
The chairman will decide whether it is debated. If accepted, a secret ballot of Labour MPs could be held on Tuesday.
Labour MPs reacted with criticism to Mr Corbyn's move to sack Mr Benn.
Shadow housing minister Roberta Blackman-Woods said: "This is sad news indeed and I cannot understand how Jeremy thinks it will help his worsening position with the PLP."
Wes Streeting, Labour's MP for Ilford North, said: "Lots of good people chose to serve in shadow cabinet to keep the show on the road. There are no longer good reasons for good people to stay."
Meanwhile, Labour former culture secretary Ben Bradshaw urged the shadow cabinet to act swiftly to "save" the party.
He said: "The Labour shadow cabinet must now act to save the party and for the sake of the country. Otherwise we will never be forgiven."
BBC political correspondent Iain Watson said Mr Benn had been publicly pretty loyal to Mr Corbyn, although the pair had disagreed over issues such as whether to extend the UK's bombing campaign from Iraq to Syria against so-called Islamic State.
But he added that losing the EU vote "tipped the balance" and Mr Corbyn had received "huge criticism" from colleagues, which was seemingly "moving up a gear" with discussions of resignations.
Dame Margaret, the MP for Barking, said Mr Corbyn should resign because the EU referendum had been a "test of leadership" that he had "failed".
She argued that Labour voters were left "not getting a clear message". In a piece for the New York Times former Prime Minister Tony Blair described Mr Corbyn as "lukewarm about remaining in the union".
On Saturday, Mr Corbyn vowed to fight off any leadership challenges and told one activist who heckled him as he attended a Pride march in London: "I did all I could."
The Labour leader vowed to ensure the party's voice was heard on workers' rights, protecting the environment and human rights in the negotiations on Britain's exit from the EU - and he suggested those negotiations should happen soon.
Quizzed afterwards about claims he had run a "half-hearted" campaign for a Remain vote, he said: "Two-thirds of Labour voters voted for Remain in response to our party's call for that."
He added: "There are some people in the Parliamentary Labour Party who would probably want somebody else being the leader of this party, they have made that abundantly clear in the past few days."
Mr Corbyn was confronted by Labour Party activist Tom Mauchline at the Pride event, who shouted: "It's your fault, Jeremy. When are you resigning? You need to resign."
However, an online petition on the website of campaign organisation 38 Degreescalling for Mr Corbyn to remain as leader has attracted more than 160,000 signatures from the general public.
In a joint statement, union leaders have also backed Mr Corbyn to continue as leader, saying the "last thing Labour needs is a manufactured leadership row of its own".
They called for Labour to "unite as a source of national stability" and challenge any attempt to use the referendum result to "introduce a more right-wing Conservative government by the backdoor".
Meanwhile, the Conservative Party faces a leadership battle of its own with former London Mayor Boris Johnson and Home Secretary Theresa May emerging as the frontrunners to replace the outgoing prime minister David Cameron, who announced he would stand down on Friday shortly after losing the EU vote.
The Sunday Times reports that Michael Gove has thrown his support behind Mr Johnson, while Cameron loyalists will favour Mrs May, who is expected to enter the leadership race in the coming days.
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