The canvas, started when he was living in Paris in 1975, depicts Hockney's face reflected in the dressing table mirror between his father and mother.
Hockney's sister, Margaret, recently opened up to the Guardian about the genesis of "My Parents and Myself," revealing that her brother's decision to abandon the project caused a brief rift with his parents.
"They would be a difficult subject matter, I'm sure. So I wasn't surprised when Mum told me in August 1976 that David had called to say he'd decided to abandon his portrait of them. Mum was naturally upset but had to respect David's decision," she explained, adding that their father was more aggravated.
Although Hockney made peace with his relatives shortly after, the artist decided to start a new version of the portrait, titled "My Parents," in 1977.
In that painting, Hockney notably depicted his father leaning over to read Aaron Scharf's 1968 book "Art and Photography," while his mother poses gracefully in a chair.
"My Parents" currently belongs to the private collection of Tate museum, after being acquired from the now-shuttered Knoedler Gallery in 1981.
The revised version of the portrait will not be included in the National Portrait Gallery's upcoming exhibition, which will run from February 27 through June 28 in London.