Boris Johnson discussed a mystery probe into "improper conduct" with Lord Geidt days before he resigned as No10’s ethics advisor.
But Downing Street is keeping the identity of the subject of the investigation secret.
Labour has urged the government to “come clean” about the “murky revelations.”
The Sunday Mirror can reveal four messages were sent between the Prime Minister's office and Lord Geidt between June 13 and June 15, when Lord Geidt resigned.
One message is understood to be a request for advice on extending steel tariffs - a potential breach of trade rules.
Lord Geidt said the request put him in an "impossible and odious position" as the measure would "risk a deliberate and purposeful breach of the Ministerial Code."
A second message is thought to be Lord Geidt's subsequent letter of resignation.
But two remaining messages remain a mystery, after Cabinet Office officials decided it would not be in the public interest to disclose them.
They confirmed they contained information about a Cabinet Office "investigation", relating to possible "conduct which is improper".
But they argued publishing the papers could prejudice future investigations.
Deputy Labour leader Angela Rayner said: “The government must come clean to the public about what exactly was said in this mystery probe. These murky revelations just raise more questions about whether Boris Johnson broke yet more rules while the rest of us were following them.
“The Cabinet Office must urgently publish the papers and come clean about what other concerns the Prime Minister’s Ethics adviser raised about Boris Johnson’s conduct.”
At the time of Lord Geidt’s resignation, it had been reported only one unresolved investigation was ongoing - into allegations of Islamophobia made by former minister Nusrat Ghani against now-Health Secretary Steve Barclay.
Mr Barclay denies the allegations, and the probe has been put on hold until Lord Geidt is replaced.
But the Cabinet Office refused to say whether the messages between Mr Johnson and Lord Geidt related to that investigation, or another undisclosed probe.
In response to a Freedom of Information request from the Sunday Mirror, a Cabinet Office official said: “If investigations into ministerial conduct were undermined and their effectiveness compromised as a consequence, it could result in conduct not being appropriately addressed, which would not be in the public interest.
“The provision of such information would, as I have set out above, prejudice the investigation process and the Cabinet Office’s ability to investigate whether any person may be responsible for improper conduct.
“There is a clear public interest in there being confidence in these investigative processes.”
