Police were called to the London home of Boris Johnson and his partner in the early hours of Friday after neighbours 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".
Mr Johnson refused to answer questions as he arrived at Birmingham ahead of the first of the Conservative Party's leadership membership hustings.
Earlier, a neighbour of Ms Symonds in Camberwell, south London, told the Guardian they had 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.
'No offences or concerns'
It said that in the recording - heard by the newspaper, but not by the BBC - Mr Johnson was refusing to leave the flat and told 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."
Another neighbour, who would only give her name as Fatima, told the BBC: "I heard a female voice, shouting and screaming, and then I heard things smashing, it sounded like plates or glasses.
"I couldn't hear what she was saying but she sounded really angry."
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."
By BBC News correspondent Helena Wilkinson
Boris Johnson would have preferred his politics - not his private life - to be making headlines.
As we enter the final stage of this leadership campaign the scrutiny of the two men who want the top job will no doubt increase.
There will be intense focus on their every move; their past, their present and their future.
It's not surprising given the importance of the job they want - running the country.
But does what allegedly happened in the London flat Mr Johnson shares with his partner really matter? His critics will say yes.
They argue that we need someone of good character who can make difficult decisions and work under pressure.
Supporters of Boris Johnson disagree. Whatever happened, they say, was an entirely private matter between two people in a relationship which should never have been recorded by a neighbour.
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."
'Would be toast'
But, political commentator Tim Montgomerie told the BBC that until a complaint was made by Ms Symonds, the row "should be a non-issue".
He added: "If there was any domestic violence, Boris Johnson's candidacy would be toast and would deserve to be.
"But all we have at the moment is a partially overheard conversation between two people late at night.
"Unless there is a complaint I think we should draw a line under this."
Some of Mr Johnson's supporters have also taken to social media to defend him.
Brexit minister James Cleverly questioned the motives of the "person who recorded Boris and then gave the story to the Guardian".
Tory MP Michael Fabricant appeared to confuse Camberwell with Islington but wrote he was glad he did not have "nosey neighbours" recording private conversations, sending them to newspapers and "wasting police time for political advantage".
Mr Johnson's relationship with Ms Symonds - a former director of communications for the Conservative party - became public after Mr Johnson and his wife announced they were divorcing in 2018.
Ms Symonds was seen in the audience during Mr Johnson's leadership campaign launch on 12 June.
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.