The 38-year-old model befriended Freud, considered one of the greatest artists of the 20th century, in 2002.
He subsequently told her how he used to give homemade tattoos using permanent ink and a scalpal when he was in the Merchant Navy during World War II.
He drew two tiny swallows at the base of her spine. Moss told Vanity Fair: ''He told me about when he was in the navy, when he was 19 or something, and he used to do all of the tattoos for the sailors.
"And I said, 'Oh my God, that's amazing.' And he went, 'I can do you one. What would you like? Would you like creatures of the animal kingdom?'
'He told me about when he was in the navy, when he was 19 or something, and he used to do all of the tattoos for the sailors.
And I said, 'Oh my God, that's amazing.' And he went, 'I can do you one. What would you like? Would you like creatures of the animal kingdom?'
''I mean, it's an original Freud. I wonder how much a collector would pay for that? A few million?"
Freud, who died in July 2011 at the age of 88, was introduced to Moss after she named him as the person should would most like to meet.
After going for dinner with him, he began painting her in the nude when she was pregnant with her daughter, Lila Grace.
She said in interviews: "I went to his house and he started [the nude painting] that night. Couldn't say no to Lucian. Very persuasive. I phoned Bella [his daughter] the next day and said, 'How long is it giong to take?'. She said: 'How big is the canvas'. I said, 'it's quite big.' She said: 'Oh dear, could take six months to a year."
In the event, the painting took nine months to complete. The model sat from 7pm to 2am, seven nights a week, and the painting was later sold to an anonymous bidder at auction for £3.9m.