It is estimated to sell for £70,000-100,000, a figure that may well tempt many investors.
Wilkie Collins's novel The Woman in White was published in 1860 and proved immensely popular - it is thought it may have provided Millais with inspiration for the painting of the sleep-walking woman.
Upon completion in 1871, the Illustrated London News commented on the figure in the painting: "Her peril as she walks with wide-open yet unseeing eyes along the verge of the sea-cliffs is intimated without the least approach to obtrusive sensationalism".
Millais (1829-1896) was a founding member of the Pre-Raphaelite Brotherhood in 1848. His later works, such as The Somnambulist, reveal the influence of the American artist Whistler.
Charles O'Brien, the head of 19th century pictures at Bonhams, comments: "This ethereal-looking work of a vulnerable girl in her delicate Victorian nightgown beautifully shows the development of Millais's later, looser style of painting."