It is understood the pair met at least once 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.
The exact nature of the talks remains unclear.
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.
The BBC reported that the discussions touched on whether photos would be revealed to the public, and that Ms Gray initiated the meeting “to clarify her intentions” for what would happen once the police investigation concluded.
But a spokesman for the Gray inquiry disputed this account of events.
They confirmed that a meeting took place, but told the PA news agency they would not characterise the talks in that way.
A No 10 source insisted the request for the meeting did not come from Mr Johnson.
“The PM did not request the meeting and hasn’t tried to influence the outcome in any way,” they said.
“It’s rightly for Sue to decide and it’s all done independently.”
It comes as about 30 people, including Mr Johnson, are being contacted by the Cabinet Office to warn them of the contents of the document ahead of its publication.
Boris Johnson must urgently explain why he held a secret meeting with Sue Gray to discuss her report
Angela Rayner, Labour’s deputy leader, called on the Prime Minister to “urgently explain” why the “secret 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.
It’s not an independent report and never has been - it’s an internal report. This isn’t a judgement on Sue Gray, it’s a statement of fact - she is an employee investigating her direct line managers https://t.co/CYNKIokNhC
— Adam Wagner (@AdamWagner1) May 20, 2022
Mr Johnson is set to be among those approached, but it was unclear on Saturday morning whether he had yet received a letter.
It was reported on Friday evening that two civil servants had indicated they were considering legal action to prevent themselves being identified in the report.
Earlier, the PM had insisted he would not seek to block names appearing in the document, and said he was “looking forward” to seeing its contents “pretty soon”.
Ms 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.”
Liberal Democrat MP Christine Jardine also called on the PM to throw light on the meeting.
“Any whiff of a stitch-up would make an absolute mockery of the report,” she said.
“This meeting must be explained. Most of the country already feels betrayed by Boris Johnson. He has undermined public trust and the public deserve a process that is completely transparent and beyond question.
“It is a sorry state of affairs that Boris Johnson and his Government are in such a crisis, he should do the right thing and resign, if not Conservative MPs should sack him.”
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.
The report is widely expected to be published next week.
The Met declined to identify anyone in its £460,000 investigation.
A team of 12 detectives examined 345 documents, including emails, door logs, diary entries, witness statements and 204 questionnaires.
They also examined 510 photographs and CCTV images.
Mr Johnson, his wife Carrie Johnson and Chancellor Rishi Sunak were all fined over the birthday gathering.
But both Johnsons were told by police they face no further action, according to Downing Street, and Mr Sunak has not received an additional fine.
The Met said 28 individuals had received between two and five fines.