Boris Johnson says there was "no interest to declare" regarding links with US businesswoman Jennifer Arcuri.
It is alleged Ms Arcuri received favourable treatment due to her friendship with Mr Johnson.
The police watchdog are deciding whether to investigate the prime minister for a potential criminal offence of misconduct in public office while he was London mayor.
Mr Johnson said everything had been done "with full propriety".
The allegations, first reported in the Sunday Times, claim Ms Arcuri joined trade missions led by Mr Johnson when he was mayor of London and that her company received several thousand pounds in sponsorship grants.
The paper has also reported Ms Arcuri told four friends that she had an affair with Mr Johnson while he was mayor of London.
On Friday, the Greater London Authority's monitoring officer referred the prime minister to the Independent Office of Police Conduct (IOPC) - whose job it is to oversee the conduct of the mayor and other members of the GLA.
Asked on the Andrew Marr show if he had declared any interest, Mr Johnson said "there was no interest to declare".
"I was proud of everything I did as mayor of London," he added.
He also attacked Sadiq Khan, the current mayor of London, 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".
Mr Johnson added that someone in his position "expects a lot of shot and shell".
Who is Jennifer Arcuri?
The woman at the centre of this story is Jennifer Arcuri, who describes herself on Twitter as an entrepreneur, cyber security expert and producer.
She began her career as a DJ on Radio Disney, before moving into film - where she wrote, produced and directed a short film that went on to be sold at Cannes Film Festival.
Ms Arcuri then brought in her tech skills to create a streaming platform for independent film makers.
But it was her founding of The Innotech Network in London that saw her path cross with Boris Johnson.
The network hosts events to discuss tech policy, and Mr Johnson was the keynote speaker at the first of those in 2012.
Since then, Ms Arcuri has also founded another company called Hacker House, which uses ethical hackers to find tech solutions for businesses.
Speaking on Sky News, Health Secretary Matt Hancock said the prime minister did not have questions to answer regarding alleged links with the US businesswoman.
"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."
But Labour leader Jeremy Corbyn said the GLA's monitoring officer had made a "wholly independent assessment" and decided there were "serious questions to answer".
In a letter to Mr Johnson, the monitoring officer set out their reasons for referring the matter to the police watchdog.
"During this time [2008 - 2016] it has been brought to my attention that you maintained a friendship with Ms Jennifer Arcuri and as a result of that friendship allowed Ms Arcuri to participate in trade missions and receive sponsorship monies in circumstances when she and her companies could not have expected otherwise to receive those benefits," it said.
The monitoring officer said it had referred the PM to the IOPC "so it can assess whether or not it is necessary to investigate the former mayor of London for the criminal offence of misconduct in public office".
It said it had recorded a "conduct matter" against Mr Johnson, which happens when there is information that indicates a criminal offence may have been committed.
But it does not mean that a criminal offence is proved in any way, the monitoring officer added.