"I think it's a good fight," said Gracie. "I think people want to see that fight. It's unfinished business and so that fight makes a lot of sense."
White revealed Thursday that St-Pierre had asked to face Diaz and the UFC boss said if Diaz agreed, they would make it happen.
GSP and Diaz were slated to meet in October 2011 for St-Pierre's welterweight title. But White yanked Diaz from the fight after he failed to show up for news conferences in Toronto and Las Vegas.
Gracie said the Diaz camp didn't have much time to talk to White about it prior to Saturday because they were getting Nate Diaz, Nick's younger brother, ready for Saturday's title bout against lightweight champion Benson Henderson.
"It didn't make sense to sit there and talk about a different fight at all," Gracie said after the televised card in Seattle. "So now that this fight's over, we can move on and move forward. We'll probably be meeting with Dana next week. It would be great to put that fight together."
Asked for his opinion on a GSP fight, Nick Diaz said: "I'm not making any comment., It's more up to Dana White."
"It's not up to me," he added. "I'm just a fighter."
Nick Diaz is currently finishing out a one-year suspension for testing positive for marijuana after his loss to Carlos Condit last February,
On Saturday, Nate Diaz lost a five-round decision to Henderson. Brother Nick was in his corner.