The Labour leader is facing a vote of no confidence 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 four-month campaign.
Senior Labour sources have also told the BBC that a significant number of shadow cabinet resignations were likely if Jeremy Corbyn were to ignore the result of the confidence vote.
Secret ballot
