It is understood the pair held at least one meeting to give an update on the document’s progress while it was being drafted but a Whitehall source said that its contents were not discussed at any point.
Such meetings would not have been viewed as unusual, the source said, with the aim to take stock of what stage the report was at.
Sky News, which broke the story, reported the meeting took place “weeks ago”.
It comes as around 30 people, including Johnson, are being contacted by the Cabinet Office to warn them of the contents of the document ahead of its publication.
Angela Rayner, Labour’s deputy leader, called on the prime minister to “urgently explain” why the meeting had taken place.
She said public confidence in the process had already been “depleted”, and people “deserve to know the truth”.
Downing Street insisted that the prime minister had been “clear throughout” that the report should be “completely independent”.
It is thought that most of the Cabinet Office letters were sent out on Thursday, as the Metropolitan Police concluded its investigation into lockdown breaches in Downing Street and across Whitehall.
Johnson is set to be among those approached but No 10 had no update as to whether he had received a letter on Friday evening.
Rayner said: “Boris Johnson must urgently explain why he held a secret meeting with Sue Gray to discuss her report despite claiming her investigation was completely independent.
“Public confidence in the process is already depleted, and people deserve to know the truth.
“This is a prime minister incapable of taking responsibility for the rotten culture he has created in Downing Street or of doing the decent thing.
“The Sue Gray report must be published in full and with all accompanying evidence.”
Adam Wagner, a human rights lawyer who has specialised in lockdown rule-breaking, said the document was “not an independent report” and “never has been”.
“It’s an internal report. This isn’t a judgment on Sue Gray, it’s a statement of fact – she is an employee investigating her direct line managers,” he tweeted.
A No 10 spokesperson said: “The prime minister commissioned the investigation led by Sue Gray and has been clear throughout that it should be completely independent.
“As he reiterated again today, the decision on what and when to publish rests entirely with the investigation team and he will respond in Parliament once it concludes.”
Not everyone contacted by the Cabinet Office will necessarily be named or identified by some other means in the report – it may merely be that their actions are referenced because they are pertinent to the narrative of a particular event.
The investigators are understood not to be including the full details of the document’s contents in the letters but instead are giving a “gist” of the relevant sections to those being approached.
Sources close to the inquiry expect the report will be published early next week.
Johnson declined to apologise again for the rule-breaking in No 10 during a visit to Hilltop Honey’s factory in Newtown in Powys, Wales, on Friday.
Asked if Downing Street would be blocking any names from appearing in the report, he said: “That will be entirely up to Sue Gray and I’ll be looking forward very much to seeing what she has to say, and fingers crossed that will be pretty soon next week.”