Sleeping by the Lion Carpet (1995-1996) is the last of four portraits the late British artist painted of Tilley, a benefits supervisor and considered among his greatest works.
Depicting her naked and sleeping in an armchair, the painting has been part of businessman Joe Lewis's family collection since 1996. It is being offered at auction for the first time at Sotheby's with a price estimate of $US33.56 million to $US46.99 million.
"It's made my life exciting," Tilley told Reuters at Sotheby's in London.
"I think that people can't believe that such a fat woman would take her clothes off and let someone paint her... I'm not really a vain person... everybody in the world is all different, all different shapes and sizes, so it's nice to have a nice big one up there."
The four canvases of Tilley, which Freud painted between 1993 and 1996, "are widely regarded not only as the artist's greatest body of work, but also among the most important, most radical and most powerful paintings of the human figure in the entire history of art," Sotheby's said.
Among the four, Benefits Supervisor Sleeping (1995), showing Tilley sleeping on a sofa, sold at auction for $US33.6 million in 2008 - at the time, a record for a work by a living artist. In 2015, Benefits Supervisor Resting (1994), depicting Tilley sitting in the corner of a sofa with her head back, sold for $US56.2 million.
"It's very rare that at auction we handle literally one of the greatest works the artist ever produced. So this is a real opportunity for a great collector and a masterpiece collector to acquire something," said Oliver Barker, chairman of Sotheby's Europe.
Sleeping by the Lion Carpet will be sold as part of the Masterpieces from the Lewis Collection London auction on June 24.
Freud, known for his nude, fleshy portraits of family, friends and himself, died in 2011.
