Sue Tilley posed for the painting over nine months in 1995
Lucian Freud's one-time muse was paid £20 a day to sit for a painting expected to fetch more than £17m.
But Londoner Sue Tilley said she did not do it for the money and had "lovely lunches" with the artist.
Freud's 1995 work, Benefits Supervisor Sleeping, looks set to become the most expensive painting by a living artist when it is sold in New York next month.
Ms Tilley - who is now a job centre manager - joked she had now become a broadsheet pin-up.
Ms Tilley - nicknamed Big Sue - told the BBC's Today programme: "I can't quite believe it, to be honest.
"I only found out on Thursday afternoon. You know, I didn't have any idea it was going to happen, so I'm a bit in shock.
"I was reading on the internet...all the things about it. And I was just going 'Oh my god', I could hardly believe it was about me."
Referring to her portrait gracing the front-page of Saturday's Financial Times, she said: "Am I the first naked pin-up in the history of the FT?
"Half the time I don't really think it's me. But then this morning I was looking at it again and I was going: 'that's my funny little face!'
Ms Tilley recreates her pose on the Today programme sofa
"The painting took nine months, but that was about two or three days a week.
"When I started I got £20 a day. I don't mind though.
"The best thing was I got lovely lunches. I got taken to the River Cafe most weekends. It was worth it for that.
"It was the experience, it wasn't the money at all.
"It was just fantastic. You know, so many people would love to have that experience, to work with such a great artist, and chat to them, find out about them and see what they were doing.
I don't worry too much, because I think even the thin girls look odd
"Because you see the painting every day, you know moving along and what he's doing and how he works on it.
"And also what I used to love was there were other paintings there as well, of other people.
"He [Lucian Freud] has about four on the go at the same time, so each time you went you'd see how far he's moved along on the other paintings as well."
When Ms Tilley was complimented by the Today presenter on being more attractive in the flesh than in the painting, she replied: "I think all his models are, it's not just me. That's why I don't worry too much, because I think even the thin girls look odd."
'Scabs and spots'
Ms Tilley has modelled for Lucian Freud on several occasions. She recalled a time overhearing a critique of her in another Freud painting.
"The man was so mortified. It was the Whitechapel Gallery. There'd been a big exhibition on and my painting had just been finished, so they put it in for the last week.
"So I went with my friends to see it, and there was this man - you know those so-called art lecturers who think they know everything - 'yes, this painting was painted because Lucian hated women, so he put the dog high up and the woman was lying on the floor. The poor thing with all her scabs and spots'.
"I started laughing. He was going 'excuse me madam' and I said, 'well actually that's me'.
"Poor man, he thought was going to fall through a hole in the floor.
"He said: 'oh but you're really pretty in real life.'"
The painting is on show at Christie's in London before being auctioned in New York.
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