The allegations, first reported in the Sunday Times on September 22, have claimed that Arcuri joined trade missions led by Johnson when he was the Mayor and that her company received several thousand pounds in sponsorship grants.
Asked during a BBC show if he had declared any interest, Johnson said "there was no interest to declare", adding: "I was proud of everything I did as Mayor of London."
He also attacked the incumbent London Mayor Sadiq Khan, saying the Labour politician "could possibly spend more time investing in police officers than he is investing in press officers and peddling this kind of stuff".
Johnson's reaction comes after it was revealed on Saturday that Johnson was referred by the Greater London Authority (GLA) to the police watchdog, the Independent Office for Police Conduct (IOPC) whose job is to oversee the conduct of the Mayor and other members of the GLA.
The reason for IOPC's involvment was because the role of the Mayor of London is also London's police and crime commissioner.
In Johnson's defence, Health Secretary Matt Hancock told Sky News on Sunday that the Prime Minister did not have questions to answer regarding alleged links with the US businesswoman, the BBC reported.
"Any monies involved went through proper due process - this was a long time ago.
"Of course, in politics, there is always squalls and there are always debates about individuals."
Arcuri, a technology entrepreneur, is believed to have moved to London seven years ago, when Johnson was Mayor.
She joined a number of trade missions led by him while in office, and it is understood she attended events on two of these trips - to New York and Tel Aviv - despite not officially qualifying for them as a delegate.
The Sunday Times reported that one of her businesses received 10,000 pounds and 1,500 pounds in sponsorship money from a mayoral organisation, as well as a 15,000 pounds government grant for foreign entrepreneurs to build businesses in Britain.
( With inputs from IANS )