Boris Johnson is expected to comply with a London Assembly order to explain his links to a US businesswoman.
Len Duvall, chairman of City Hall’s oversight committee, said: “We are going to get something this evening from Downing Street.”
The PM is facing questions about his friendship with Jennifer Arcuri when he was London mayor.
He has been accused of failing to declare a conflict of interest, but has said he acted properly at all times.
Mr Johnson had been given until Tuesday to provide details of contacts with Ms Arcuri.
Mr Duvall said: “We have had some fun and games today arguing about when is the deadline, but we finally have an announcement that they are going to comply, and we are going to get something this evening from Downing Street. I hope it is comprehensive and I hope it provides answers.
“The allegations are serious, I hope the prime minister is treating them seriously.”
He said the assembly’s powers to take action against Mr Johnson, if he was found to have breached its code of conduct, were limited because he was no longer mayor of London.
He held the office between 2008 and 2016.
But it could still summon the prime minister to appear before the oversight committee to answer further questions about his contacts with Ms Arcuri, along with others connected to the case.
The committee has asked for the details and a timeline of all contact between Mr Johnson and Ms Arcuri, including private text messages and emails.
According to the Sunday Times, which first reported the story, Ms Arcuri joined trade missions led by Mr Johnson when he was mayor and received thousands of pounds in public money.
It is also understood she attended events on two of the trade missions – to New York and Tel Aviv – despite not officially qualifying for them as a delegate.
The prime minister has denied breaking any rules of conduct and insisted everything was done “entirely in the proper way”.
Ms Arcuri told ITV’s Good Morning Britain Mr Johnson was “a really good friend” – but denied the then mayor had shown any “favouritism” towards her.
The code governing conduct at London City Hall states that public office holders should not act in any way to gain benefits for families or friends, and should declare private interests to resolve any conflicts.
Mr Duvall, a Labour member of the London Assembly, said his committee was attempting to “make a judgement call on what the relationship was” before deciding what, if any, action it would take at a meeting next week.
Separately, the Independent Office for Police Conduct has been asked to consider whether Mr Johnson, who as mayor was responsible for policing in London, should be investigated for misconduct in public office, a criminal offence.
Current Mayor Sadiq Khan has asked a senior lawyer to review a 2013 decision by London and Partners, the mayor’s promotional agency, to sponsor a conference organised one of Ms Arcuri’s companies, for £10,000.
London and Partners say they have found no evidence of Mr Johnson’s involvement in the decision.
The Department for Culture, Media and Sport is, meanwhile, “reviewing” a £100,000 grant made in February this year to Ms Arcuri’s cyber-security business Hacker House.