The work and pensions secretary left open the option of a joint ticket with the candidate she famously said was not “the man you want driving you home at the end of the evening”.
Asked about the criticism – made during the 2016 Brexit referendum campaign – Ms Rudd described it as “a phrase that continues to haunt me”.
But, asked if it meant she could not back Mr Johnson, she replied: “I’m not going to be drawn on any individual candidates and I’m afraid that does include Boris.”
The work and pensions secretary had previously appeared to distance herself from a so-called Bamber alliance, which Mr Johnson – still the favourite to succeed Theresa May – is keen to foster.
Speaking to the BBC, she also left open the option of running for leader herself, despite the widespread belief that a pro-EU candidature is doomed to fail.
“What I’ve said is that I’m not planning to run, so I have kept the door slightly ajar, but I’m not committed to it at the moment,” she said.
During the live TV debate three years ago, Ms Rudd poured scorn on Mr Johnson’s discredited claim that leaving the EU would allow the UK to hand £350m a week more to the NHS.
“I fear the only number Boris is interested in is the one that says Number 10,” she told millions of viewers.
And she added: “He’s the life and soul of the party but he’s not the man you want driving you home at the end of the evening.”
Asked by Radio 5 Live’s Emma Barnett if some of Mr Johnson’s comments should rule out support from the One Nation group, Ms Rudd said his remarks on women wearing niqabs, were “completely inappropriate”.
“That is an area we would certainly want to test him on,” she said.
But she added: “The area that we really disagree on is how we leave the European Union, and that’s one of the key areas that I would start with with any leadership candidate.
“And I know that other members of the One Nation group feel the same. We have to do it in a way that protects the economy and jobs.
“So what we oppose – not everybody in the One Nation caucus, but almost everybody – is leaving without a deal, which we think would be damaging.”
Ms Rudd also said she believed the talks with Labour on a compromise Brexit deal could bear fruit, saying: “It feels like Labour are engaging seriously.”
She added: “It will be very disappointing if it turns out it was all a charade.”