•Both the Metropolitan and Thames Valley Police say they are assessing the information received.
•The public inquiry, which is separate to the privileges committee probe, will begin hearings next month.
Boris Johnson has been referred to police by the Cabinet Office over further potential rule breaches during the Covid pandemic.
The department said it made the referral after a review of documents ahead of the Covid public inquiry.
The former PM, who was fined last year for breaking Covid rules in 2020, has strongly denied wrongdoing.
Both the Metropolitan and Thames Valley Police say they are assessing the information received.
The Cabinet Office said officials had been obliged to disclose the documents to the police under civil service rules.
The Times, which first reported the story, says Mr Johnson has been referred to Thames Valley police because his ministerial diary revealed visits by family and friends to Chequers - the prime minister's country house in Buckinghamshire - during the pandemic.
Thames Valley Police said it had "received a report of potential breaches of the Health Protection Regulations between June 2020 and May 2021 at Chequers, Buckinghamshire".
The Met Police released a similar statement but said their information related to potential breaches in Downing Street.
It is understood Mr Johnson has had no contact from the police.
The spokesman for the former prime minister said it was "totally untrue" that there had been further Covid rule breaches.
"The events in question were all within the rules either because they were held outdoors or came within another lawful exception. They include regular meetings with civil servants and advisers.
"It appears some within government have decided to make unfounded suggestions both to the police and to the Privileges Committee - many will conclude that this has all the hallmarks of yet another politically motivated stitch up.
The spokesman said Mr Johnson's lawyers had written to the Cabinet Office, as well as the Commons Privileges Committee, "explaining that the events were lawful and were not breaches of any Covid regulations".
The seven-member committee of MPs has been investigating whether Mr Johnson misled Parliament over Covid rule-breaking events in government buildings.
In a statement, the committee said it had received additional evidence from the government last week and asked Mr Johnson for a response, both of which it would now take into account during its probe.
If the committee concludes Mr Johnson deliberately misled MPs over the events, he could potentially face a suspension from Parliament, which in turn could lead to a by-election in his Uxbridge and South Ruislip constituency.
Mr Johnson's spokesman also said it was "bizarre and unacceptable" that "no contact was made with Mr Johnson before these incorrect allegations were made both to the police and to the Privileges Committee". The Cabinet Office has denied the suggestion Mr Johnson was not given prior notice.
The Cabinet Office said the material it had passed to police came from the "normal" process of reviewing documents to be submitted to the public inquiry into the government's handling of the pandemic.
"In-line with obligations in the Civil Service Code, this material has been passed to the relevant authorities and it is now a matter for them."
The BBC has been told the matter was not considered by ministers or the cabinet secretary, who heads the civil service.
The public inquiry, which is separate to the privileges committee probe, will begin hearings next month.
Responding to the announcement, Labour's deputy leader Angela Rayner said: "These new allegations are for the police to examine but the government must explain who else knew at the time and why this has only now come to light."
Liberal Democrat deputy leader Daisy Cooper, said Mr Johnson "should finally do one decent thing and consider his position as an MP".
Lindsay Jackson, spokesperson for Covid-19 Bereaved Families for Justice, said Mr Johnson was "totally unfit for any form of public service, never mind being the prime minister".
But, speaking on his GB News programme, Conservative MP and former minister Jacob Rees-Mogg defended Mr Johnson, saying: "The latest stories are just another example of how those who don't like Boris, mainly because of Brexit, are always looking for something to have a go at him on."
Mr Johnson resigned as prime minister last July, in part due to public anger over revelations he broke Covid lockdown rules.
In April 2021 he received a fine from the police for breaking lockdown rules after attending a gathering on his birthday in June 2020.
And, in May 2022, a report by then-senior civil servant Sue Gray set out a series of social events held by staff in Downing Street which broke the rules.