The "Hot N Cold" singer was whisked away to Thailand on a romantic break with the presenter after impressing him with a picture of her breasts after they met at the MTV Video Music Awards last month.
A source said: "When they were both in New York for the music awards Russell finally got his chance to work his charm on her."
"Katy knows his bad boy reputation but could not resist – especially when Russell sent her a love poem with a note attached saying, 'Please send me a poem back.'"
"Russell couldn't stop laughing when Katy sent a photo of her boobs with the word 'poem' scrawled across them."
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"The next minute Russell picked up the phone and invited her to Thailand for a secret getaway."
Friends have warned Katy about the 34-year-old comic's womanizing ways but she is determined to make the relationship work.
The source told Britain's The Sun newspaper: "Despite his reputation, Katy thinks Russell is so charming she just wants to give things a go with him. She thinks he is hilarious and incredibly sexy."
The couple have now returned from their trip, with Katy taking to her Twitter page to gush about the "magical" holiday.
Speaking about some of Russell's favorite stars, she added: "Been schooled on Morrissey, Oscar Wilde and Peter Sellers."
Russell also used Twitter while on holiday, revealing he had been looking at "sexy" statues in Thailand.
Katy and Russell were first romantically linked after the VMA awards when they were seen kissing at Lady Gaga's after-party at New York nightspot Avenue.
Meanwhile, it has been announced that Katy will host the MTV Europe Music Awards (EMAs) next month.
The 24-year-old star impressed bosses after she fronted the ceremony in Liverpool, England, last year and so they have asked her to return for next month's show in Berlin.
Katy is the first person to front two consecutive EMAs.
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