It follows claims that shortly before being given the job, Mr Sharp helped the then-prime minister, Boris Johnson, secure a loan guarantee agreement.

Mr Sharp, Mr Johnson and the government all deny there was a conflict of interest.

But Labour has asked the parliamentary standards watchdog for an inquiry.

Labour has suggested that Mr Johnson could have breached the code of conduct for MPs "through failing to appropriately declare the arrangement" on his Parliamentary register of interests.

According to the Sunday Times, which first reported the claims, Mr Sharp was involved in helping to arrange a guarantor on a loan of up to £800,000 for Mr Johnson in late 2020.

Mr Sharp said he had "simply connected" people, while Mr Johnson's spokesman said the report was "rubbish" and insisted his financial arrangements "have been properly declared".

On Sunday, the Cabinet Office also rejected the accusations there had been a conflict of interest. Conflicts of interest are when there might be a clash between an MP or minister's public duties, and their private interests.

"Richard Sharp was appointed as chairman of the BBC following a rigorous appointments process including assessment by a panel of experts, constituted according to the public appointments code," a Cabinet Office spokesperson said.

"There was additional pre-appointment scrutiny by a House of Commons Select Committee which confirmed Mr Sharp's appointment. All the correct recruitment processes were followed."

The Sunday Times story centres on events in late 2020, when Mr Johnson was reported to be in financial difficulty.

It says multimillionaire Canadian businessman Sam Blyth - a distant cousin of Mr Johnson - raised with Mr Sharp the idea of acting as Mr Johnson's guarantor for a loan. It is not clear where the loan agreement itself came from.

Mr Sharp - a Conservative Party donor who at the time was applying to be the chairman of the BBC - contacted Simon Case, the then-cabinet secretary and head of the civil service. The paper says a due diligence process was then instigated.

On Sunday afternoon a Cabinet Office spokesperson backed this up, saying: "Mr Sharp reminded the cabinet secretary about the BBC appointment process and asked for advice given his existing relationship with Boris Johnson.

"They agreed that he could not take part in discussions involving the then prime minister, given the appointment process. This was accepted by Mr Sharp to avoid any conflict or appearance of any conflict of interest and the then prime minister was advised accordingly."

According to the Sunday Times, Mr Sharp, Mr Blyth and Mr Johnson had dinner together at Chequers before the loan guarantee was finalised, although they deny the PM's finances were discussed then.

Mr Sharp - a former Goldman Sachs banker - was announced as the government's choice for the new BBC chairman in January 2021.

The government's choice is ultimately decided by the prime minister, on the advice of the culture secretary, who is in turn advised by a panel.

As BBC chairman, Mr Sharp is responsible for upholding and protecting the BBC's independence, and ensuring it fulfils its mission to inform, educate and entertain. Candidates for publicly-appointed roles such as the chairman job are required to declare any conflicts of interest.

Labour's chairwoman Anneliese Dodds has written to the Parliamentary Commissioner for Standards, Daniel Greenberg - who is in charge of regulating MPs' conduct - asking for "an urgent investigation into the facts of this case".

Ms Dodds said she was concerned that Mr Johnson may have breached rules "by asking for an individual to facilitate a guarantee on a loan whom he would later appoint to a senior public role".

She said that a "lack of transparency" may "give the impression that this was a quid pro quo arrangement, something which would undermine the integrity of the democratic process, and calls into question the process by which the chairman of the BBC was appointed".

On Sunday morning, Foreign Secretary James Cleverly said Mr Sharp was appointed on merit.

Mr Sharp declined to appear on BBC One's Laura Kuenssberg on Sunday but told the programme "the claim that there was anything financial involved is not true".

What has Richard Sharp said?

"There is not a conflict when I simply connected, at his request, Mr Blyth with the cabinet secretary and had no further involvement whatsoever."

What has Mr Johnson said?

A spokesman for Mr Johnson said: "Richard Sharp has never given any financial advice to Boris Johnson, nor has Mr Johnson sought any financial advice from him. There has never been any remuneration or compensation to Mr Sharp from Boris Johnson for this or any other service.

"Mr Johnson did indeed have dinner with Mr Sharp, whom he has known for almost 20 years, and with his cousin. So what? Big deal.

"All Mr Johnson's financial arrangements have been properly declared and registered on the advice of officials."

What has the government said?

A Cabinet Office spokesperson said: "Richard Sharp was appointed as chairman of the BBC following a rigorous appointments process including assessment by a panel of experts, constituted according to the public appointments code.

"There was additional pre-appointment scrutiny by a House of Commons Select Committee which confirmed Mr Sharp's appointment. All the correct recruitment processes were followed.

"The recruitment process is set out clearly and transparently in the governance code on public appointments and overseen by the Commissioner for Public Appointments."

What has the BBC said?

"The BBC plays no role in the recruitment of the chair and any questions are a matter for the government."