The natural history TV presenter struck up a friendship with the 'It's Oh So Quiet' singer when they filmed a documentary together in which they explore music in nature, entitled 'Attenborough and Bjork: The Nature of Music', and David admits he finds the Icelandic pop star mesmerising.
David - who admits he can't pronounce Bjork's name properly - revealed: ''I called her 'honey' [while filming]. She is really quite enchanting.''
The 86-year-old TV star and Bjork, 47, got on so well they worked together on another project with David recording a spoken-word introduction for her album 'Biophilia', which incorporated live exhibitions and iPad apps.
In the documentary the broadcaster reveals his own passion for music and introduce footage of the lyre bird, reed warbler and blue whale to show the music that exists in the animal kingdom.
Bjork is not the first famous women to catch the eye of David.
He added to The Sun newspaper: ''The camera angle made it look as if I was sitting on her lap, or vice-versa. It wasn't quite like that!
''Well, I like the company of human beings, and they are more than 50 per cent of the population, so yes. I like the company of women.''
David can next be seen on TV screens in 'Galapagos 3D with David Attenborough' which will be broadcast on New Year's Day (01.01.13) at 7pm on Sky 3D and in 2D on Sky 1HD.