In a letter addressed to Johnson and dated September 23, Len Duvall, chairman of the London Assembly GLA (Greater London Assembly) Oversight Committee said he wanted the "details and a timeline of all contact" with Jennifer Arcuri "including social, personal and professional during his period of office as Mayor of London", the BBC reported on Tuesday night.
He also asked for "an explanation of how that alleged personal relationship was disclosed and taken into account in any and all dealings with the GLA".
The committee has the legal power to summon Johnson to appear before it for questioning and has done once before - when it quizzed him over the failed Garden Bridge project in 2018.
The development comes after The Sunday Times said that Arcuri joined trade missions Johnson had led and received thousands in sponsorship grants.
Arcuri told the paper any grants she received and any trade missions she joined were "were purely in respect of my role as a legitimate businesswoman".
On Monday evening, when asked about the allegations, Johnson told the BBC: "All I can say is I am very proud of what we did as Mayor of London... particularly banging the drum for our city and country around the world.
"I can tell you that absolutely everything was done entirely in the proper way."
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 when Johnson was Mayor, as well as a 15,000 pounds government grant for foreign entrepreneurs to build businesses in Britain.
( With inputs from IANS )