The painting by the Spanish artist depicts a morose-looking nude cabaret singer with red lips and brown curly hair, contrasting with her unhealthy pale skin.
Conservation work uncovered hidden under the lining on the reverse of the painting a portrait of Picasso's anarchist friend and art dealer Pere Manach.
"The whimsical and wicked rendering depicts the dealer wearing an exotic headdress, with his head on a female body in a dancer's leap," Sotheby's said in a statement.
"La Gommeuse" is estimated at some $60 million (53 million euros) and is due to be auctioned in New York, where it will be put on display from October 30.
The painting is a rare one from the artist's Blue Period that is not in a museum.
It was painted in 1901 by a 19-year-old Picasso -- a year after he arrived in Paris.
Koch, brother of conservative mega-donors Charles and David Koch, bought the painting in 1984.
Picasso's masterpiece "Les Femmes d'Alger" became the most expensive painting ever sold at auction when it went for $179.36 million at Christie's in New York in May.
The previous record had been held by Francis Bacon's "Three Studies of Lucian Freud" which sold for $142.4 million at Christie's in New York in 2013.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.