Portrait Of An Artist (Pool With Two Figures) will be auctioned at Christie’s in November and has been estimated at $80 million (£61m).
The previous record was set by Jeff Koons’s Balloon Dog, which sold for $58.4 million (£45m) in 2013.
The 1972 painting by Hockney, 81, is “the holy grail of his paintings, from both the historical and the market perspectives”, said Alex Rotter, co-chairman of post-war and contemporary art at Christie’s in New York.
“It has all the elements that you would want in a Hockney painting,” Mr Rotter said. “The California landscape, the beautiful trees and flowers and the sky, and then what we know him most for, which is the pool.”
The painting has been held by a private collector, and “we have been trying to get it for a very long time” Mr Rotter said.
The work depicts two men - one swimming breaststroke under water, the other standing by the pool looking down - and was inspired by two photographs Hockney found on his studio floor, one of a swimmer in Hollywood in 1966, and another of a boy staring at something on the ground.
The standing figure is said to represent Peter Schlesinger, whom the artist met in 1966, when the younger man was a student in one of Hockney’s art classes at UCLA.
For the next five years, according to Christie’s, he was both “the great love of Hockney’s life” and one of his favourite models.
The relationship ended in 1971. Hockney had already begun the painting and he abandoned it, starting again the following year.
Mr Rotter said with Hockney “one of the last of his generation still standing, and also painting, this painting will likely be the most expensive work by a living artist sold at auction.”