Boris Johnson wrote a letter recommending Jennifer Arcuri for a job as the head of a technology quango when he was mayor of London, it has been reported.

The prime minister has been embroiled in a conflict of interest row since details of the pair’s close relationship emerged last month.

The US businesswoman accompanied Johnson on three overseas trade missions led by the then mayor, after initially being turned down for two of them. Her companies were also awarded £126,000 of public money.

According to the latest revelation, Johnson was listed as a reference on Arcuri’s application for a role at Tech City, which was launched by David Cameron to bolster digital companies in east London.

The Sunday Times said Arcuri was a 27-year-old student when she applied for the £100,000 a year job in 2012.

In an email leaked to the newspaper, she allegedly later wrote: “I still have the letter of rec from Boris. hahaha. To think that we asked him to write us a recommendation for the CEO of Tech City is just hysterical.”

Arcuri did not get the job, which went to Joanna Shields, a former head of Facebook in Europe, the Middle East and Africa.

Johnson and Arcuri have both refused to deny they had an affair but the technology entrepreneur has said the stories being written about her are false, without being more specific.

On Monday, she will give her first television interview since the row erupted by appearing on ITV’s Good Morning Britain, according to the show’s co-presenter, Piers Morgan.

On Thursday, a US lawyer claiming to act on behalf of Arcuri said he was inviting media outlets, including British publications, to bid six-figure sums for an interview with her.

California-based Michael Walsh said five outlets were in the running for an interview with $225,000 (£202,000) the highest bid at that time.

In an interview with Bloomberg on Friday, Arcuri said: “I will not be the person to bring Boris Johnson down. I refuse to be a pawn.”

She said she was within her rights to go on the trade missions and apply for the grants received by her companies, insisting “my relationship with Boris is nobody’s business”.

Several inquiries have been opened since the allegations emerged. The Greater London Authority has asked the Independent Office for Police Conduct to assess whether Johnson, as a former police commissioner, should face a criminal investigation for misconduct in public office.

The prime minister has until Tuesday to respond to a summons from the London assembly to provide details of his relationship with Arcuri.