But Ms Badenoch slammed the suggestion, accusing the former chairman of “disgraceful misrepresentation”.
She also told MPs in the Commons on Monday (February 20) that there was "no evidence whatsoever that this is true".
"For Henry Staunton to suggest otherwise, for whatever personal motives, is a disgrace and it risks damaging confidence in the compensation schemes that ministers and civil servants are working so hard to deliver," she said.
"I would hope that most people reading the interview in yesterday's Sunday Times would see it for what it was: a blatant attempt to seek revenge following dismissal."
Mr Staunton had said that Ms Badenoch told him that “someone’s got to take the rap” for the Horizon scandal and that he discovered his sacking after a phone call from Sky News.
Mr Staunton, who began his role in December 2022 following nine years as WH Smith chairman, had told the newspaper: “Early on, I was told by a fairly senior person to stall on spend on compensation and on the replacement of Horizon and to limp, in quotation marks — I did a file note on it — limp into the election.
“It was not an anti-postmaster thing, it was just straight financials. I didn’t ask, because I said ‘I’m having no part of it – I’m not here to limp into the election, it’s not the right thing to do by postmasters’.
“The word ‘limp’ gives you a snapshot of where they were.”
My call with Staunton was with officials. They took a complete record.
He has given an interview full of lies about our conversation during his dismissal.
The details will emerge soon enough as I won’t let the matter rest here, but will be discussing with govt lawyers. (3/5)
— Kemi Badenoch (@KemiBadenoch) February 18, 2024
Ms Badenoch, in a lengthy post on X, said: “Henry Staunton had a lack of grip getting justice for postmasters. The serious concerns over his conduct were the reasons I asked him to step down.
“That he chose to run to the media with made-up anecdotes and a series of falsehoods, confirms I made the correct decision.”
She said her call with Mr Staunton “was with officials” who took a “complete record”.
“He has given an interview full of lies about our conversation during his dismissal.
“The details will emerge soon enough as I won’t let the matter rest here, but will be discussing with (Government) lawyers,” she said.
This is Henry Staunton’s reply to Kemi Badenoch.
Firstly, with regard to the comment made to Mr Staunton by the senior civil servant to the effect that he was to stall on compensation payments to Horizon victims and on spend on the
Horizon replacement so the government could…
— Robert Peston (@Peston) February 19, 2024
This was her second denial in as many months after she was forced in January to deny claims that she was being lined up to replace Rishi Sunak, saying Tory plotters "need to stop messing around".
The Guardian reported that Ms Badenoch thought it was wrong to end the prime minister's tenure, despite his polling figures.
Ms Badenoch also told Sky’s Sunday Morning with Trevor Phillips that Mr Sunak needed the support of the party as it prepared for an election.
She said: “They need to stop messing around and get behind the leader.
“The fact of the matter is most people in the country are not interested in all of this Westminster tittle-tattle. Quite frankly, the people who keep putting my name in there are not my friends. They don’t care about me. They don’t care about my family or what this would entail. They are just stirring."
Here’s who Kemi Badenoch is.
How did Kemi Badenoch become business and trade secretary?
Olukemi Olufunto "Kemi" Badenoch, to give her full name, has had a long career within the Conservative party and has been tipped consistently for big things.
Becoming the Conservative MP for Saffron Walden in 2017, she served as international trade secretary before taking up her current role.
In 2022, she put herself forward to replace former prime minister Boris Johnson as a “fresh face” for the Tories. Ms Badenoch showed her right-wing credentials by standing on an anti-woke and small government platform.
“There are always tough choices in life and in politics; no free lunches, no tax cuts without limits on government spending, no stronger defence without a slimmer state,” she said at the time.
Her bid was backed by more than a dozen Tory colleagues, including Michael Gove. However, she ultimately lost out to Liz Truss in the Tory party leadership campaign, finishing fourth.
Ms Badenoch, 44, had been international trade secretary since September 2022 and was previous minister of women and equalities.
Her promotion was part of a wider departmental shake-up, with the prime minister splitting the Department for Business, Energy and Industrial Strategy into three new departments.
The move was made as part of a restructuring that began with the departure of Nadhim Zahawi as party chairman.
What is Kemi Badenoch’s political background?
Born in Wimbledon, Ms Badenoch lived in the US and Nigeria as a child before returning to the UK aged 16.
She has talked about working at McDonald’s while studying for her A-levels in Morden.
After graduating from the University of Sussex with a master's degree in computer systems engineering, she worked for companies including the Royal Bank of Scotland, private bank Coutts, and the Spectator magazine.
She joined the Conservative party in 2005, aged 25.
Five years later, she stood as the Tory candidate in Dulwich and West Norwood, coming third in the vote won by Labour's Tessa Jowell.
In 2012, she stood for the Conservatives in the London Assembly election.
The party won only three seats and Ms Badenoch came fifth on the London-wide list, behind Suella Braverman in fourth, meaning she was not elected.
At the 2015 general election, City Hall Tory Victoria Borwick was elected as an MP and resigned her seat on the London Assembly.
Ms Braverman, who contested the Tory leadership alongside Ms Badenoch, also won a seat in the House of Commons that same year and declined to fill the vacancy.
Ms Badenoch was therefore called on to take up the seat in City Hall in September 2015. She went on to retain it at the 2016 London Assembly elections. She was the London Tory spokesman for the economy and also sat on the transport committee and policing and crime committee.
In the 2017 election, she stood in the safe Conservative seat of Saffron Walden in Essex and was elected to Parliament.
She has described herself as an example of the “British dream”, an “immigrant who came to the UK aged 16 and who became a parliamentarian” in one generation. She cites Winston Churchill and Margaret Thatcher as two of her heroes.
Her father, Femi Adegoke, was a GP and her mother, Feyi Adegoke, was a professor of physiology.
What was Kemi Badenoch’s position on Brexit?
Ms Badenoch was a supporter of Brexit. In a rousing maiden speech in Parliament, she described the referendum as “the greatest ever vote of confidence in the project of the United Kingdom”.
Her banker husband, Hamish, a former Merton Conservative councillor, was a staunch Remainer.
“We have had robust arguments but respect each other’s view,” Ms Badenoch told the Independent in 2017.
Ms Badenoch was criticised for publicly shaming journalist Nadine White in 2021.
The HuffPost reporter had asked the equalities minister’s office about suggestions Ms Badenoch had refused to participate in a video featuring black cross-party politicians seeking to promote the Covid-19 vaccination.
Screenshots of Ms White’s two emails were shared on Twitter by Ms Badenoch, who branded them “creepy and bizarre”. Labour called for an investigation and Ms White said the MP’s actions set a dangerous precedent, threatening the role of a free press.
Ms Badenoch has admitted hacking Harriet Harman’s website in 2008 as part of a “foolish prank”. She had guessed the Labour MP’s password and then posted a hoax blog post claiming that the then-minister for women and equality was supporting Boris Johnson in the London elections.
In 2018, she told Core Politics: “About 10 years ago I hacked into… a Labour MP’s website and I changed all the stuff in there to say nice things about Tories.”
In May 2023, Sir Lindsay Hoyle was unhappy that the announcement of a U-turn on scrapping EU laws after Brexit had been made in the form of a written statement to MPs rather than being presented to the House of Commons.
During the debate, Sir Lindsay snapped: “Who do you think you’re speaking to?”. This was after Ms Badenoch had said she was sorry the timing of the announcement was “not to your satisfaction”.
MPs also criticised Ms Badenoch for her “tin ear” and “patronising” approach in response to questions over the Retained EU Law (Revocation and Reform) Bill.