Scotland Yard chief Sir Bernard Hogan-Howe is set to meet Lord Brittan's widow, following criticism of the handling of a rape allegation against her late husband.
The Metropolitan Police commissioner will apologise to Lady Brittan at a meeting at a central London hotel on Tuesday, according to reports.
Britain's largest police force came under fire over its handling of an allegation that Lord Brittan raped a 19-year-old woman known as "Jane" in 1967.
The politician died in January last year without being told he would not face any action over the claim.
In October police apologised to Lady Brittan, saying she should have been informed in April that there would not have been a prosecution had her husband been alive.
The Met declined to comment on reports about the meeting.
It comes amid intense scrutiny of the Operation Midland, a separate inquiry into allegations of a VIP paedophile gang.
As well as historical abuse claims, the investigation is also examining allegations that three young boys were murdered.
There have been suggestions that the inquiry, which had cost £1.8 million as of November, is on the brink of collapse.
Claims emerged on Monday that police believe the central witness in the investigation, a man known as "Nick", is still credible but have not uncovered evidence to support criminal charges against any suspects.
Detectives have not been able to disprove Nick's credibility nor establish that his central claims could not have happened, according to The Guardian.
It reported that officers believe witnesses who may be able to help prove or disprove the claims are yet to come forward, adding that no specific dates of alleged attacks have been established, nor has any direct evidence of murder been uncovered, or specific links to homicide victims.
It was also reported that the investigation has so far not uncovered enough evidence against a living person to reach the standard of reasonable suspicion necessary to make an arrest.
A furore erupted over Operation Midland after D-Day veteran Lord Bramall was cleared of historical abuse allegations.
His home had been raided and he was interviewed under caution before he was told in January he would face no further action.
Former Tory MP Harvey Proctor, who furiously denied any involvement, has been interviewed under caution twice. There have been reports that he will be formally told he will face no further action.
The late former prime minister Edward Heath has also been named in connection with the inquiry.
When the investigation was launched, a detective described Nick's account as "credible and true".
The force later acknowledged the description had "suggested we were pre-empting the outcome of the investigation".