The 29-year-old star, who ended her engagement to vegan chef Matthew Mosshart in January, jokingly said she is in a new relationship with the 'Australia's Next Top Model' judge, but later admitted they could be true.
Osbourne, who flew to Sydney to be a guest judge on the reality TV show, initially played coy when asked if she is dating the US-born model, 29, on the 'Kyle and Jackie O Show'.
Cohen then joined the interview and admitted, "We've known each other for a bit and we really enjoy ourselves with each other... And it bloomed a little bit."
Osbourne was most recently linked to model Ricki Hall and they were spotted attending her father Ozzy Osbourne's gig in London in July.