Speaking to "UFC Unfiltered" on Tuesday, White said he would like to see the matchup co-headline UFC 227 at Staples Center in Los Angeles.
"We are working right now to try and put together a GSP-versus-Nate Diaz fight," White told the podcast. "It is true, and they would fight at 155 pounds."
Neither St-Pierre nor Diaz has publicly discussed a potential fight, although ESPN reported last week that Diaz has been in serious negotiations to appear on the UFC 227 card. He has not fought since a high-profile rematch against Conor McGregor in August 2016.
According to White, in a "perfect" world, the Aug. 4 pay-per-view event would consist of a previously announced bantamweight title fight between TJ Dillashaw and Cody Garbrandt, St-Pierre versus Diaz, and a light heavyweight bout between Alexander Gustafsson and Luke Rockhold. The latter two fights have not yet been agreed to.
The UFC's longest-reigning welterweight champion, St-Pierre (26-2) returned from a four-year layoff to defeat Michael Bisping for the middleweight championship in November.
Arguably the greatest fighter of all time, St-Pierre, 36, vacated the 185-pound title just 33 days after winning it, citing medical concerns. He has been sidelined this year with ulcerative colitis, and also stated he will only return to the Octagon for legacy fights at this point in his career.
St-Pierre, who trains in Montreal, has never fought in the UFC at 155 pounds.
Diaz (19-11) is in the midst of the longest layoff of his career. The California native has expressed interest in returning to the UFC this year.
Nick Diaz, Nate's older brother and a former Strikeforce champion, challenged St-Pierre for the UFC title in March 2013. St-Pierre defended his title via unanimous decision.