Letters between Boris Johnson and his independent standards adviser on who paid for the refurbishment of his Downing Street flat will be published next month, the BBC has been told.
The Financial Times has reported that the prime minister will be cleared of breaking the ministerial code and misleading adviser Lord Geidt.
Labour said Mr Johnson had “made a mockery of the standards the public has a right to expect”.
Downing Street declined to comment.
The Cabinet Office, which co-ordinates government policy, said it would not comment on speculation.
Lord Geidt cleared the prime minister in May of a conflict of interest after it emerged that Conservative peer Lord Brownlow had donated £52,000 to help cover the costs of the refurbishment of his flat above No 11 Downing Street.
But the adviser revisited his inquiry after new information emerged, to see if he had been misled by the prime minister.
The Financial Times reported that, while Mr Johnson is set to be criticised in the fresh probe, he will be cleared of breaking the ministerial code, which sets rules for conduct in office. The newspaper also suggested he would not be found to have deceived his adviser.
In May, Lord Geidt said the prime minister appeared not to be aware that Lord Brownlow had contributed from his own pocket.
But in December, the Electoral Commission said in a report that Mr Johnson had sent a WhatsApp message to Lord Brownlow in November 2020 to ask for extra money.
Downing Street argued that the prime minster was “not aware of the underlying details” of Lord Brownlow’s donations, when asked about the apparent discrepancy between what he told Lord Geidt and what the Electoral Commission said.
His spokesman said Mr Johnson had thought Lord Brownlow was overseeing the money, but he did not realise the peer was providing the money himself.
When the apparent discrepancy emerged, the BBC was told Lord Geidt was unhappy but was not considering quitting. However, Labour’s deputy leader Angela Rayner accused the prime minister of lying to the public.
On Thursday, the Financial Times quoted anonymous senior officials as saying the prime minister’s conduct would be “criticised” and that Lord Geidt had now seen all the relevant WhatsApp messages between Mr Johnson and Lord Brownlow.
The BBC has been told that a series of letters between the prime minister and Lord Geidt will be published on the government’s website in early January.
A spokesperson for the Cabinet Office, where Lord Geidt’s office is based, said they would not comment on speculation, but added: “The terms of reference set out that advice the independent adviser provides to the prime minister on matters which are referred to him will be published in a timely manner.”
Ms Rayner said: “After the Electoral Commission ruled that the Conservative Party broke the law on declaring donations, the prime minister has made a mockery of the standards the public has a right to expect.
“While the British public is facing a cost-of-living crisis, Boris Johnson is busy writing to his own adviser about why he did not give him all of the information he needed for his investigation.”
She called for all the correspondence between Lord Geidt and the prime minister to be published “as a first step towards providing full transparency into how Boris Johnson is explaining away his WhatsApp messages with Tory donors”.
“It is embarrassing that when the country needs real leadership, Boris Johnson is busy trying to clear up his own personal mess,” she added.