The Observer newspaper, citing sources, said that government officials gave the new Prime Minister informal advice as he drew up his Cabinet in October regarding the risks from an HMRC investigation settled only months earlier.
Mr Sunak has faced questions about his decision to appoint Mr Zahawi as Tory chairman, with questions too asked about his political judgment in doing so.
He has insisted that “no issues were raised with me” when he appointed Mr Zahawi to his current role.
Downing Street strongly denied the report, as the row over Mr Zahawi and his tax affairs continues.
A Number 10 spokesperson said: “These claims are not true. The Prime Minister was not informed of these details, informally or otherwise.”
The paper reports the claim that Mr Sunak was warned that the tax issue involved a significant amount of money.
It comes after the Prime Minister ordered an investigation into Mr Zahawi by Sir Laurie Magnus, his independent adviser on ministers’ interests, following a report in The Guardian that the Tory chairman had paid a penalty as part of the dispute.
But pressure continues to build on Mr Zahawi, with one unnamed Cabinet minister telling The Sunday Telegraph: “I think he’s got to go.”
He has so far resisted calls to stand aside, just as Mr Sunak has resisted calls to sack him.
The same minister told the paper that Mr Sunak was still right to refer the party chairman to Sir Laurie, adding: “If he’d have sacked him you’d have had the constant refrain of ‘it wasn’t natural justice’.”
Mr Zahawi is believed to have authorised HMRC to discuss his settlement – estimated to be worth £4.8 million including the penalty – with the ethics inquiry.
Mr Sunak this week told broadcasters: “I’m not going to pre-judge the outcome of the investigation, it’s important that the independent adviser is able to do his work.
“That’s what he’s currently doing, that’s what I’ve asked him to do and I’ll await the findings of that investigation.”
A week ago, Mr Sunak told Prime Minister’s Questions that Mr Zahawi had addressed the fiasco “in full”.
But he went on to launch an investigation, admitting there were “questions that need answering” after the penalty was revealed.
Deputy Labour leader Angela Rayner urged Mr Sunak to “come clean”.
She said: “The Prime Minister’s pathetic attempt to dodge scrutiny and skirt responsibility over Nadhim Zahawi cannot hold. He must now come clean on what he knew and when.
“The first hundred days of Rishi Sunak’s premiership have revealed a Prime Minister too weak to lead.”
Lord Young of Cookham, who served in a range of Conservative administrations from Margaret Thatcher to Theresa May, also appeared to suggest that Mr Zahawi should step away from his Conservative Party role while the inquiry into his tax affairs continues..
Speaking to BBC Radio 4’s Week In Westminster programme, Lord Young said: “Last year, a minister was accused of an impropriety. He resigned and he was cleared.”
In an apparent reference to former minister Conor Burns, who had the Tory whip restored after being cleared of misconduct at the party conference in October, he said: “I think what a prime minister should do in those sorts of circumstances is bring the minister back and I think that would give out a signal that (it) is not the end of your career if you stand back while the inquiry takes place.
“You can be rehabilitated if, indeed, allegations are proved to be untrue,” said the peer, who chaired the Standards and Privileges Committee for nearly a decade.
Lord Young said that he hoped the inquiry into Mr Zahawi would not “take too long”.
He also called for the report into Mr Zahawi to be published “in full”, as well as adding his voice to calls for the Government’s ethics adviser to be able to initiate their own investigations.
Lord Young said: “I think a signal would be if that report was published in full. We’ve been promised a summary. Well, I’d quite like to see the whole report.”
It comes amid reports too of frustration within the Conservative Party towards Cabinet Secretary Simon Case, with claims that he must shoulder some of the responsibility for the row erupting around Mr Zahawi, as well as the controversy surrounding Boris Johnson, BBC chairman Richard Sharp and a reported loan facility of up to £800,000.
A Cabinet Office spokesperson said: “The Cabinet Secretary is focused on ensuring that the Civil Service and the whole of Government is working together to deliver for the British people.”
On Saturday, HMRC admitted that it had made mistakes in the handling of a freedom of information (FOI) request centred on the tax affairs of ministers.
The Financial Times reported that in response to an inquiry by the paper last year, HMRC said that no minister was being investigated.
But at the time, Mr Zahawi was the subject of a probe by tax officials.
We acknowledge that the processing of this FOI request was subject to a series of administrative errors, which we very much regret
The paper reported that a response to a freedom of information request by tax lawyer Dan Neidle, who had been working to expose Mr Zahawi’s tax affairs, was believed by HMRC staff to be incorrect after he was informed that it was a backbench Tory MP and not a minister who was under investigation.
“We acknowledge that the processing of this FOI request was subject to a series of administrative errors, which we very much regret.
“We corrected these errors as soon as they came to light and are confident that our most recent response to Mr Neidle was both accurate and in line with the Information Commissioner’s Office guidance,” an HMRC spokesperson said.
Amid the furore over his tax arrangements, Mr Zahawi visited a barbershop in his constituency on Friday, posting photos of the engagement on Twitter on Saturday morning.