Former model Jennifer Arcuri, 34, is in the spotlight in the United Kingdom amid allegations she received money and perks from London coffers while Johnson was mayor of the British capital.
She said she saved Mr Johnson's number in her telephone under the name "Alex the Great", and revealed he visited her flat a "handful" of times - later clarifying that meant five.
"I'm not answering", Arcuri told ITV's Good Morning Britain, after presenter Piers Morgan asked her repeatedly whether she'd had an "intimate" relationship with Johnson during his time as London Mayor.
Mr Johnson has said he will comply with the London Assembly's request but added: "On this particular matter, I think they are barking up the wrong tree".
Johnson has strenuously denied any impropriety during his tenure as London mayor.
USA businesswoman Jennifer Arcuri has revealed that she asked PM Boris Johnson - whose number she saved in her phone as "Alex the Great" - whether he would like to be shown "a few things" on a pole in her flat. "Categorically, Boris has nothing to do with all of my other achievements". Boris never ever gave me favouritism.
"But Boris is extremely personable".
Mr Johnson is accused of not declaring a personal interest despite the pair having a friendship.
"I'm never going to tell you that", she smiled.
"It's really categorically no-one's business", she added. "I would love to ask you a few questions".
Mr Johnson has, however, said there was "no interest to declare", telling the BBC's Andrew Marr that "everything was done with full propriety". "But I wish him well, I want him to be happy".
The report adds to mounting questions about the Prime Minister's past links with Ms Arcuri.
London Mayor Sadiq Khan launched an independent review into how Arcuri managed to accompany Johnson on government-sponsored trade missions in 2014 and 2015 to Singapore, Tel Aviv and NY, and why the American won sponsorship from the city's London & Partners promotional group when Johnson was mayor.
Despite the mayor's backing, Ms Arcuri is not believed to have been shortlisted for the role.
"Regardless of the exact nature of his relationship with Arcuri, it is clear that she and Boris Johnson were close, and that he misled the public when he said "there was no interest to declare", McDonnell said in a statement. I don't need him right now, Britain needs him right now".
The corruption scandal intensified over the weekend as the Sunday Times published emails appearing to show Mr Johnson wrote a letter of recommendation for Ms Arcuri to be head of a technology quango when he was London mayor.
But Mr Johnson insisted last week that everything he did when promoting London overseas as mayor was done in "complete conformity with the code and the rules".
If he fails to respond to the request he could be summoned by the Assembly.
Since then, Ms Arcuri has also another company, Hacker House, which uses ethical hackers to find technology solutions for businesses.
The flat and office of Ms Arcuri's company at 134 Shoreditch High Street which Mr Johnson reportedly visited several times.
In the latest charge, a new London Sunday Times columnist said that when Johnson served as editor of the conservative weekly magazine, the Spectator, he groped her upper thigh during a boozy staff luncheon in the late 1990s.