The masterpiece will likely make waves at Sotheby's Contemporary Art evening auction, which will take place on February 11 in London.
"The Splash" is the second in a series of three canvases initiated in 1966, in which Hockney explores his lifelong fascination with the texture, appearance and depth of water.
The work on sale at Sotheby's is a close sister to "A Bigger Splash," which belongs to the collection of the Tate museum in London.
Although the two paintings slightly differ in their compositions, both were created at a watershed moment in Hockney's career, during which the Yorkshire-born artist relocated to an apartment-studio in Los Angeles.
Between the summers of 1966 and 1967, Hockney created "The Splash" and several of his most recognizable works, such as the privately-owned "Little Splash."
The inspiration for "The Splash" notably came from a photograph he saw in a Hollywood magazine on how to build swimming pools, immortalizing the moment just seconds after a diver has broken the surface of the turquoise water.
"I loved the idea of painting this thing that lasts for two seconds; it takes me two weeks to paint this event that lasts for two seconds. Everyone knows a splash can't be frozen in time, so when you see it like that in a painting it's even more striking than in a photograph," Hockney once said of his "Splash" series.
Now going under the hammer at Sotheby's London, "The Splash" is estimated to sell for between £20 million and £30 million (around $26 million and $39 million).
This presale high estimate is far from Hockney's current auction record of $90.3 million, which was set in November 2018 at Christie's New York for his famed "Portrait of an Artist (Pool with Two Figures)."
At the time, Hockney momentarily became the most expensive living artist, before being dethroned a few months later by Jeff Koons with the $91.1 million sale of his "Rabbit."
Ahead of Sotheby's Contemporary Art evening sale on February 11, "The Splash" will go on view at soon-to-be-announced dates at Sotheby's galleries in Hong Kong, Taipei, New York and London.