The notebook, which likely dates back to 1942, is thought to be from the period of Turing's life which inspired the plot of the Oscar-nominated The Imitation Game.
Benedict Cumberbatch played Turing - who led a team of cryptanalysts to break the German enigma codes from his workshop at Bletchley Park during WW2.
Turing's code breaking activity shortened the war by two to four years, saving as many as 14m lives according to some academics.
While Turing should have been hailed as a hero, seven years after the end of the war he was arrested and convicted of gross indecency for homosexual activity. He was not pardoned until 2013.
To avoid going to jail, Turing underwent chemical castration, the effects of which led him to commit suicide in 1954.
"[The notebook is] probably the most extensive manuscript that exists in Turing's hand," Cassandra Hatton, senior specialist in fine books and manuscripts and the history of science at Bonhams told the Financial Times.
“To be able to look in and see his thought processes is extremely important — you see the types of things in mathematics that really bothered him, what he thought needed to be worked on.”
Alan Turing's notebook will be sold on behalf of an anonymous vendor in New York on April 13 at Bonhams.