Davison has already posed for the magazine’s German edition and is currently in talks with Hugh Hefner about an American appearance.
The Sunday Independent reports that Hef was taken with Davison when he invited the former Miss World to his infamous Playboy Mansion.
The paper says the legendary playboy took the Irish model on a private viewing around his luxury pad before they enjoyed a private dinner and watched a movie together, a traditional Friday night activity for Hefner and his playmates.
The report says the 87-year-old Playboy founder initially took a shine to Davison when he saw her shoot for German Playboy.
A source told the Sunday Independent: “He absolutely loves the idea of Rosanna being the first Miss World to appear in Playboy USA. They are yet to hammer out a deal – but I’d say, watch this space.”