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The Independent Office for Police Conduct is currently assessing whether to investigate Johnson over a potential criminal offense of misconduct in public office.
The Sunday Times reported last week that a company run by Arcuri received tens of thousands of pounds in public funding when Johnson was mayor.
When asked by the BBC's Andrew Marr on Sunday if he declared his friendship with Arcuri, the Prime Minister said "everything was done in accordance with the code (of conduct)" and that "everything was done with full propriety."
"Allegations have been brought to the attention of the Monitoring Officer that Boris Johnson maintained a friendship with 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," the statement said.
The Independent Office for Police Conduct is involved because Johnson was in charge of the Metropolitan Police as part of his role as mayor, said the statement.
Arcuri and her company have not responded to CNN's request for comment. She told the Sunday Times, "any grants received and any trade mission I joined were purely in respect of my role as a legitimate businesswoman."
The GLA also released a letter it sent to the Prime Minister, informing him it has referred the issue to the police watchdog.
The letter also lists three international trade missions in which Arcuri allegedly took part. According to the letter, she was allowed to take part in two even though her companies did not qualify. She participated in the third one after re-applying following an initial rejection.
CNN's Nada Bashir contributed to this article.