The 1955 painting will appear in a newly launched evening sale of 20th century art entitled 'Looking Forward to the Past'.
The current record for any object sold at auction is $127m (£83m), a sum set by Francis Bacon's Three Studies of Lucian Freud which sold at Christie's New York in November 2013.
The consignment comes 18 years after Les femmes d'Alger (Version 'O') last came to auction in the same rooms as part of the landmark sale of the Victor and Sally Ganz collection. In November 1997, it was estimated at $10-12m and sold for $29m (£17.1m).
The 3ft 9in x 4ft 10in (1.14 x 1.46m) oil on canvas is part of a series of 15 works that Picasso based on Delacroix's Les femmes d'Alger (designated as versions A to O). Picasso also conceived the series as a eulogy to Henri Matisse who had died five weeks before he began the series. Matisse had viewed Delacroix as his immediate forebear in terms of colour and Orientalist subject matter, while Picasso sought to carry this legacy forward, saying: "When Matisse died, he left his odalisques to me as a legacy."
The sale of the Ganz collection was a seminal event both for Picasso and the wider market. The auction had five Picassos which fetched over $10m. The $206.5m (£121.5m) premium-inclusive total doubled the previous high for a single-owner auction at the time.
Les femmes d'Alger (Version 'O') was the second highest-selling lot in the sale.
The top lot was Picasso's Le Rêve, a portrait of his mistress Marie-Thérèse Walter which took $44m (£25.8m) - a picture which was later acquired by Steve Wynn in 2001 before the American casino magnate accidentally punctured the canvas with his right elbow in 2006, just after he had agreed to sell it to fellow American collector Steve Cohen for $139m. After it was repaired, Cohen remained interested in the portrait, finally acquiring it from Wynn in a reported $155m deal in 2013.
The performance of Les femmes d'Alger (Version 'O') in the upcoming sale will give an indication of whether Picasso's 1950s pictures can achieve the kind of sums which are currently the reserve of works from the early 1930s. Le Rêve dates from 1932, the same year as the painting that holds the current auction record for Picasso, Nude, Green Leaves and Bust, which was knocked down at $95m (£65.1m) at Christie's New York in May 2010.
Les femmes d'Alger (Version 'O') will be the highlight of Christie's ' Looking Forward to the Past' sale which will include about 25 lots created between 1902 and the end of the century. The auctioneers will offer a mixture of paintings, drawings, and sculpture by artists including Claude Monet, Piet Mondrian, Egon Schiele, Marcel Duchamp, René Magritte, Picasso, Jean Dubuffet, Mark Rothko, Alexander Calder, Martin Kippenberger, and John Curri.
Christie's head of post-war and Contemporary art Brett Gorvy said: "Today our most powerful clients globally are assembling collections that are characterized by the outstanding quality of individual objects rather than specific periods or national movements."