Some 14,000 members of the Conservative Party want Mr Johnson’s name to be on the ballot as Rishi Sunak and Liz Truss battle it out for the leadership.
The petition has been organised by Tory peer Lord Cruddas and former MEP David Campbell-Bannerman.
And, at a hustings in Leeds on Thursday evening, claps and cheers were heard as the host referenced the report.
Asked what he would say to those members, Mr Sunak said: “I’d say to them that I think close to 60 people resigned in Parliament and it’s incumbent on the Prime Minister to have the confidence of the parliamentary party, and that wasn’t there at the end.
“So whether he’s on the ballot or not, ultimately you need to be able to command the confidence of your MPs in Parliament, and we got to a point where close to 60 of them had resigned from Government.”
Rishi Sunak said he's been having 'the time of his life' while campaigning
Owen Humphreys
Liz Truss answering questions in Leeds
Owen Humphreys
Ms Truss, meanwhile, focused her pitch on transport – and pledged to get a Northern Powerhouse rail line built.
She said: “I remember as a teenager getting the bus into Leeds city centre because there was no other alternative. I’m afraid, my friends, it’s not much better now.
“Leeds is still the largest city in Europe without its own metro network, and I would work to fix that.”
Referencing her upbringing in the city, she said it was “fantastic” to be in her “old stomping ground”, adding that she hoped none of her former teachers were in the audience.
Ms Truss said she got “grit, determination and straight-talking” from Yorkshire, and that is what is needed in Downing Street as “we face a huge global economic crisis”.
Whereas the former Chancellor said he was “having the time of my life” campaigning.
Speaking to host Nick Ferrari at the LBC event, he outlined his vision to tackle NHS waiting lists, “grip” inflation, and “restore trust, rebuild the economy, reunite our country”.
He said: “This campaign has been absolutely brilliant. I have been having the time of my life over the last week being out and about across the country, talking to all of you, talking to all our members.
“We will cut VAT on fuel. But what I won’t do is embark on a spree borrowing tens and tens of billions of pounds of unfunded promises and put them on the country’s credit card, and pass them on to our children and our grandchildren to pick up the tab.
“That’s not right. That’s not responsible, and it’s certainly not Conservative.
"But of course, once we grip inflation and ensure that mortgage rates don’t rise and cripple people, I’m going to cut taxes.”