Police were called to the London home of Boris Johnson and his partner in the early hours of Friday after a neighbour reportedly heard a loud argument.
The Guardian said Carrie Symonds was heard telling the Conservative MP to “get off me” and “get out of my flat”.
The Metropolitan Police told the BBC it “spoke to all occupants of the address, who were all safe and well”.
In a statement, it said “there was no cause for police action”. A spokesman for Mr Johnson said: “No comment”.
The Guardian reported that a neighbour had told the newspaper they heard a woman screaming followed by “slamming and banging”.
The paper said the neighbour was inside their own flat when they recorded the alleged altercation.
It said that in the recording – heard by the Guardian, but not by the BBC – Mr Johnson was refusing to leave the flat and telling the woman to “get off” his laptop before there was a loud crashing noise.
Ms Symonds is allegedly heard saying the MP had ruined a sofa with red wine: “You just don’t care for anything because you’re spoilt. You have no care for money or anything.”
‘No offences or concerns’
Conservative MP Dominic Grieve told BBC Radio 4’s Today programme he could not comment on the Guardian’s report specifically but said character was relevant in the contest to be leader of the party.
“They are going to be in a position of responsibility where they have to make very important decisions,” he said.
The former attorney general added: “Clearly, things like reliability and honesty are very important things.
“And I think they matter in one’s private and personal life, and also they matter in one’s public life.”
BBC deputy political editor John Pienaar said questions about Mr Johnson’s private are hovering over the leadership contest.
He said: “It’s a question of his judgement, decisions that he’s made and how they might inform the way that he takes decisions in the future.
“It’s not just of immediate importance, it bears on the way the country might be run from 10 Downing Street at such a critical point in the country’s history.”
Journalist Sonia Purnell, who has written a biography of Mr Johnson, told the Today programme she believed it was important to know a future leader’s character.
She said: “It is the most unbelievably pressured job, crises will be coming at you day and night. You have to have equilibrium, a clear head, a stability in your life to be able to cope with that.”
But Daily Telegraph journalist Allison Pearson asked: “What right do we have to listen in to a private lovers tiff?”
She told the programme: “The Tory members won’t care about this. They’ve been waiting since 2016 to vote for Boris Johnson.”
In a statement, the Metropolitan Police said: “At 00:24 on Friday 21 June, police responded to a call from a local resident in the SE5 area of Camberwell.
“The caller was concerned for the welfare of a female neighbour.
“Police attended and spoke to all occupants of the address, who were all safe and well. There were no offences or concerns apparent to the officers and there was no cause for police action.”
Mr Johnson is the bookmakers’ favourite to succeed Theresa May as Conservative leader and the UK’s next prime minister.
The former foreign secretary and Mayor of London is in a run-off with Jeremy Hunt, with Tory party members due to vote over the next month.
Mr Johnson came top in a ballot of Tory MPs on Thursday. The first hustings of the second phase of the leadership campaign takes place on Saturday.