Francis Bacon's Two Figures will star in a sale at Christie's London on February 11 with a valuation of £5m-7m ($7.1m-9.9m).
The work was painted in Paris in the mid-1970s, following the suicide of Bacon's long-term partner George Dyer, and depicts the two men entwined - watched by a dwarf-like figure.
Bacon gave the work as a gift to his friend and confidante, the art critic Michael Peppiatt, in 1976. However he later decided he was not happy with the composition.
He cut the painting in two, separating the lovers from the dwarf and creating two paintings. The work has been in Peppiatt's collection ever since.
The other piece, featuring the dwarf, was sold on.
Francis Outred, chairman and head of post war and contemporary art at Christie's, explained: "This work is not only a memorial of Bacon's great love but also a testament to the relationship between artist and writer.
"The extraordinary story of the painting's evolution and how it came into Michael's collection is unlike any other.
"The long-standing friendship between Peppiatt and Bacon is one of rare depth and Michael's recollections of this period allow a fascinating insight into the life and working of one of the greatest painters of the twentieth century."
Bacon's Three Studies for a Portrait of Lucian Freud remains one of the most valuable paintings ever sold, achieving a record $142.4m in 2013 at Sotheby's.
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