The Queen supported EU withdrawal in the run-up to the referendum, it has been claimed.
Laura Kuenssberg, the BBC's political editor, said she was told about the alleged comment months before the eventual appearance of The Sun's "Queen backs Brexit" headline in March.
The front page story caused one of the biggest rows of the referendum campaign, leading to a successful complaint to press regulator Ipso by Buckingham Palace, which said it was "misleading".
The Sun stood by its story, saying it had two sources for the claim that the Queen had "let rip" at then deputy prime minister Nick Clegg about Europe at a lunch at Windsor Castle.
Mr Clegg has named then justice secretary Michael Gove as the source of the story, but Mr Gove has never confirmed the allegation.
Ms Kuenssberg said that her "jaw hit the floor" when an unnamed contact told her that the Queen had told a private lunch that she could not see why Britain could not simply leave the EU.
The BBC political editor told BBC Radio 4's Today programme: "In a casual chat with one of my contacts, they said 'Do you know what? At some point this is going to come out, and I'm telling you now and I don't know if the BBC would touch it, but the Queen told people at a private lunch that she thinks that we should leave the EU'.
"Apparently at this lunch she said 'I don't see why we can't just get out. What's the problem?'
And a row ensued. "My jaw hit the floor. Very sadly, I only had one source. I spent the next few days trying to prove it. I couldn't find the evidence.
"Lo and behold, a couple of months later, someone else did. Of course then ensued a huge row between that newspaper and the Palace over what had really been said or not said.
"There were lots of moments in the referendum campaign but for me that was one when my jaw did hit the floor. Very frustratingly, the story did eventually emerge, whether it was true or not."
