Ann Widdecombe has said doesn't want to debate because she doesn't want to put her edge in the Conservative Party leadership contest at risk.
The have closed in the vote for the Tories' new leader, with Ms Badenoch and Mr Jenrick going head-to-head to replace Rishi Sunak.
The result will be announced on Saturday after a leadership contest which has lasted nearly four months.
Ms Badenoch, 44, was widely believed to have won a TV clash against Mr Jenrick which aired on last month.
Ms Widdecombe, writing for the same broadcaster, said on Thursday that Ms Badenoch was denying Tory members and the public another head-to-head debate with her opponent.
Reform UK's immigration spokesperson wrote: "Believing herself to have the edge, she does not want to put it at risk by facing an opponent who has come up with policies such as making overseas aid dependent on countries accepting back their nationals who have arrived here illegally."
She suggested that because the two leadership contenders have spent a relatively short space of time in parliament, the outcome of the contest "comes down to who can talk the better game" rather than who is able to do the job of leading the Conservative Party.
Ms Widdecombe continued: "Whatever the outcome, the Tories will be led from the right, assuming Jenrick's conversion from centrist to right is genuine. That means Reform UK has won the agenda in the same way that the Tories forced Blair to adopt their policies in 1997."
Former immigration minister Mr Jenrick, 42, has put leaving the European Convention on Human Rights at the centre of his campaign.
During the Conservative Party conference, he faced heat from other leadership rivals over claims he made about the UK's special forces.
Nicknamed "Robert Generic" when first elected to the Commons in 2014, he has gradually shifted to the right.
Ms Badenoch held a number of ministerial positions under both Liz Truss and Mr Sunak and was business secretary before the Tories lost power in July.
She also held the women and equalities brief and made a name for herself as an outspoken voice on gender issues, including by calling for a change to the Equality Act so that sex is defined only as someone's biological sex.
A survey of Tory members by the ConservativeHome website last week suggested Ms Badenoch had the lead, by 55 percent to 31 percent.
Donations to Mr Jenrick's campaign totalled £480,000 and Ms Badenoch has received £422,500 over the course of the campaign, according to the latest Register of MPs' Interests.
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