The Independent Office for Police Conduct (IOPC) will consider whether there are grounds to investigate the Prime Minister for potentially committing misconduct in a public office by allegedly giving Ms Arcuri favourable treatment while he was mayor of London.
Mr Johnson has denied allegations relating to his friendship with technology entrepreneur Ms Arcuri, which first emerged last weekend.
On Friday the Greater London Authority (GLA) said its monitoring officer had recorded a "conduct matter" against Mr Johnson over allegations.
The move, which came on the eve of the Tory Party conference in Manchester, has been dismissed by Downing Street as a "nakedly political put-up job".
A senior Government source said no evidence had been provided to support the allegations, and the Prime Minister had been given no opportunity to respond before a GLA press statement was released late on Friday.
The source said: “Due process has not been followed and the timing is overtly political. The public and media will rightly see through such a nakedly political put-up job.”
In a statement, the GLA said: “The 'conduct matter' has been recorded as 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.
“A 'conduct matter' exists where there is information that indicates that a criminal offence may have been committed. It does not mean that this is proved in any way. The IOPC will now consider if it is necessary for the matter to be investigated.”
A No 10 spokesman said: “The Prime Minister, as mayor of London, did a huge amount of work when selling our capital city around the world, beating the drum for London and the UK. Everything was done with propriety and in the normal way.”
Earlier Mr Johnson said that he would comply with an order by the London Assembly to provide details of his links with Ms Arcuri, although he insisted they were "barking up the wrong tree".
The allegations relating to Ms Arcuri first emerged in The Sunday Times and suggested that she was given £126,000 in public money and given privileged access to three foreign trade missions led by Mr Johnson while he was mayor.
The Government has since frozen a £100,000 grant to Ms Arcuri's company, Hacker House, pending a review.