Labour is calling for an investigation after allegations surfaced in The Sunday Times.
The newspaper reports that Tory donor Richard Sharp was involved in talks about financing Mr Johnson in late 2020.
Mr Sharp is believed to have introduced multimillionaire Canadian businessman Sam Blyth – a distant cousin of Mr Johnson, who had proposed to act as the then-PM’s guarantor for a credit facility – to the former prime minster.
According to the Sunday Times, the three men then had dinner at Chequers before the loan was finalised.
Mr Sharp, a former Goldman Sachs banker, was announced as the government’s choice for the BBC chairman role in January 2021.
Mr Johnson was recently given a £1million donation by tech investor Christopher Harborne, it has emerged.
Mr Johnson toured war-damage in Kyiv yesterday. As PM he was accused of using visits and calls to Ukraine president Volodymyr Zelensky to distract from domestic problems.
Labour has now written to the Parliamentary Commissioner for Standards Daniel Greenberg, demanding an investigation.
Party chair Anneliese Dodds cited the MPs’ code of conduct that ‘holders of public office should not place themselves under any financial or other obligation to outside individuals or organisations that might influence them in the performance of their official duties’.
She added: ‘Serious questions need to be asked of Johnson: why has this money never been declared, and what exactly did he promise these very generous friends in return for such lavish loans?’
When contacted, a BBC spokesman said: ‘The BBC plays no role in the recruitment of the chair and any questions are a matter for the Government.’