The British comedian and his US pop star girlfriend were reportedly "messing around" in a Los Angeles studio where they recorded a version of Edward Lear`s 1871 poem `The Owl and the Pussycat`.
A source told Britain`s The Sun newspaper: "Russell was just messing around in the studio with Katy.
"He was pretending to sing into the microphone and started reciting the poem, `The Owl And The Pussycat`, with the lines, `Oh lovely Pussy! Oh Pussy my love, what a beautiful Pussy you are`."
The poem is said to be a private joke between the pair, after Russell, 34, recited it to `I Kissed A Girl` singer Katy, 25, when they holidayed together in Thailand.
The source added: "They often use the nicknames Owl and Pussycat. Russell is `Owl` because he`s wise and, well, it`s fairly obvious that Katy`s a sex kitten, isn`t it?
"He has an amazing delivery. Katy blushed at the line, `O let us be married, too long have we tarried` then joined in, singing a refrain to Russell`s speech.
"That`s when it dawned on everyone. It was actually really good. With work, it could be a really interesting track, evocative of The Goons or Monty Python. They were very harmonious. Everyone was transfixed."
Russell has previously sung in the film `Forgetting Sarah Marshall` in which he played rock star character Aldous Snow. A follow-up film in which he will reprise the role, `Get Him To The Greek` - in which Katy makes a cameo appearance - is set for release in summer next year.