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) and is due to be auctioned in New York, where it will be put on display from October 30th.
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.