Lawyers told a High Court judge on Friday that both sides had agreed to pause the legal fight for one month.
Sir Cliff is suing the BBC and South Yorkshire Police over coverage of the 2014 raid.
Lawyers for the singer previously said he had suffered "profound and long-lasting" damage from the incident.
Mr Justice Mann, who has been overseeing the preliminary hearings at the High Court in London, indicated that he would review matters in the near future.
Sir Cliff was investigated over historical sexual assault allegations, which he denied, and the case was dropped by the Crown Prosecution Service in June last year because of insufficient evidence.
The singer is seeking "very substantial" compensation because he says the coverage of the raid at his apartment in Sunningdale, Berkshire, invaded his privacy.
BBC editors have previously apologised for distress but have said they will "defend ourselves vigorously".
A spokeswoman said the BBC had reported Sir Cliff's "full denial of the allegations at every stage".
South Yorkshire Police have apologised "wholeheartedly for the additional anxiety caused" by the force's "initial handling of the media interest" in its investigation into the singer.

President Cecile Richards told members of Congress on Tuesday she was "proud" that Planned Parenthood donates foetal tissue for research.
The anti-abortion group behind the videos has alleged that the healthcare provider profits from the practice.
The allegations have set off an effort to pull the group's federal funding.
Ms Richards said foetal tissue donation is legal and noted its small role in what Planned Parenthood does.
Planned Parenthood has said it charges small fees - between $30 (Â£20) and $100 - to cover processing costs, but does not make a profit from foetal donations.
"These outrageous accusations based on videos are offensive and untrue," Ms Richards said. "But facts have never gotten in the way of campaigns to keep women from getting healthcare."
Planned Parenthood is a non-profit group that provides reproductive health services to mostly lower-income Americans. Some of its locations perform abortions.
Federal funds make up about 40% of its annual budget, but federal law prohibits the funding of abortions except in rare cases.
Conservative Republicans in Congress have threatened to shut down the government in hopes of ending federal support for Planned Parenthood.
However, Republican congressional leaders have opposed a shutdown and President Obama has vowed to veto any attempt to defund Planned Parenthood.
During a hearing on Tuesday, Republican lawmakers scrutinised the organisation's finances and chided Ms Richards for her salary, travel budgets and the organisation's rate of health screenings.
Representative Elijah Cummings, a Democrat, said he was in full support of keeping the organisation funded.
"For many poor women, Planned Parenthood may be one of their only services of medical care in underserved or rural communities," he said.
"Big question for my Republican colleagues: Do you really want to do this? Align yourself with radical extremists who manipulate the facts?"
Some lawmakers told Ms Richards that Planned Parenthood's funding should be re-directed toward other US health clinics that would supposedly provide more services.
"The taxpayers... have a right to know how this money is being spent," said Representative Cynthia Lummis, a Republican from Wyoming.
"They have a right to know if if taxpayer dollars are being used to free up services you provide that are abhorrent services in the view of many taxpayers when there are alternatives in this country."
Republicans argued during the hearing that those other health centres across the US would be able to handle the influx of patients should Planned Parenthood lose its funding.
Representative Brendan Boyle, a Democrat from Pennsylvania, said he disagreed and that unintended pregnancy and abortion rates would actually go up if Planned Parenthood ceased to exist.
Citing a Congressional Budget Office study, he said that 390,000 women in the US would lose access to health care without Planned Parenthood.
Both anti-abortion activists and Planned Parenthood supporters could be seen on Capitol Hill on Tuesday, with many wearing pink T-shirts to show their support for Ms Richards' organisation.
Sir Cliff Richard and the BBC have agreed to try to reach a settlement over coverage of a police raid on the singer's home.
[NEXT_CONCEPT]
The head of Planned Parenthood has defended her organisation before Congress, calling a series of secretly recorded videos a "smear campaign".