"I just don't know, I'm amazed he's doing it, I really am.”
Under the plan being considered in Mr Corbyn’s office, Lord Falconer will be appointed as the party’s antisemitism surveillance commissioner, with full oversight of how Labour handles complaints.
“There's a lot of criticism he's doing it but I don't know the answer,” said Lord Levy. “Undoubtedly, Charlie will call and speak to me, I will have a better judgement when he does.
"I've known Charlie since I really got involved at a top level - 28 years ago."
Asked about his decision to retain close links to the Labour leadership at a time when relations with the Jewish community are at their lowest ebb, Lord Levy, who is Tony Blair’s former fundraiser, said: “This whole thing has been driving me meshuga, I have not been sleeping at night.
“"I'm going to do my hardest, the truth is I'm actually getting sick over it, I mean physically sick.
"It is driving me nuts - my wife said 'Michael you are nearly 75. You have given your life to this whole community - what are you doing to yourself?'
"It is really horrible. Can I make a difference? I'm going to do my damnedest to try and do so."
Lord Levy said Monday's meeting, where Lord Mandelson and John Reid were standing behind him, had “moments when you just want to get up and punch somebody.”
The Labour Peer said his head was “swimming” after attending the Parliamentary Labour Party meeting where Mr Corbyn revealed he would support a second referendum deal if he cannot get the Brexit deal he wants.
But the issue of the party’s antisemitism crisis also remained high on the agenda at the two-hour meeting.
“Louise Ellman, David Blunkett were very strong,” said Lord Levy.
“There were a number of people who spoke that were very, very strong about the direction of the party, against antisemitism and the mixed messages - the way the people that left the party were vilified."
During the meeting, Lord Blunkett rounded on the leadership over their failure to stem the antisemitism crisis and said he did not want to see the party led by “old fashioned Marxists.”
Dame Louise, who is on the verge of quitting after being subjected to a vicious campaign of intimidation by pro-Corbyn loyalists in her local party, voiced her anger at the leadership.
Dame Margaret Hodge said Mr Corbyn was in “denial” over the scale of the Jew-hate problem in the party – while another Peer called for the leader to visit Luciana Berger’s Wavertree constituency and tell local members they were wrong and had not acted in his name when she faced repeated bullying that led her to quit the party last week.
Lord Levy said Ms Berger was a “special lady” and added it was "totally out of order the way people who had left the Party were being treated".
He added the party's treatment of her was "disgraceful".
Asked about Dame Louise, Lord Levy said : "She looked very sad, very sad indeed. She spoke about how the antisemitism wasn't being dealt with.
"I was on the other side and frankly I felt like giving her a big hug."
