The session was “part of a package” fixed with all of the political parties, he said, with Mr Johnson earmarked to be quizzed in the next few days it is understood.
The claim goes further than previous suggestions that Mr Johnson has gone back on a commitment – because, it is widely believed, he fears the damage from facing the aggressive questioning by Mr Neil.
It was made as the prime minister again refused to commit to the interview, with the Conservatives still claiming that negotiations are ongoing.
Mr Corbyn, speaking on the campaign trail in Leeds, linked the controversy to wider Tory dirty tricks that were bringing “politics and democracy into disrepute”.
Revealing the talks with BBC, the Labour leader said: “I agreed to take part in one-to-one debates with the prime minister.” The second will be staged on Friday next week.
He then added: “We also agreed, as part of that package, that all party leaders would be subject to an interview with Andrew Neil.
“I had my interview with Andrew Neil, the other party leaders have had some of their interviews, but the prime minister decided not to do so.”
“Don’t go around playing these stupid games of trying to bring out false information purporting to come from somebody else,” he said, in front of an audience in Leeds.
“This is what brings politics and democracy into disrepute.”
The BBC has been accused of “abject surrender” after first refusing to allow Mr Johnson to appear on The Andrew Marr Show unless he also fixed a date for Andrew Neil – before dropping the demand.
The corporation claimed that was in the public interest, after the London Bridge terror attack, but it inevitably meant there was limited time for other election topics.
On the show, Mr Johnson again refused to commit to a date – despite the election now being just 11 days away.
“I am perfectly happy to be interviewed by any interviewer called Andrew from the BBC,” he said, but stopped short of confirming it would take place.
The Independent understands that the agreement was for Mr Johnson to be interviewed within the next few days, one week after the Labour leader’s bruising clash with Mr Neil.
The Conservative Party has been asked to respond to the allegation that an agreement has been broken.