The purpose of the sitdown was to clear the air about any old grievances that may have existed between the two when they were with Phoenix in the mid-2000s, according to sources.
Stoudemire then attended the Yankees' game against the visiting Blue Jays, sitting behind the plate, according to New York media reports. He was to appear later at an annual July 4 party hosted by Knicks owner James Dolan, the reports said.
While helping the Suns become one of the league's best and most exciting teams, D'Antoni and Stoudemire clashed hard and often, leading several executives around the NBA to insist the two would never consider working together again.
On Sunday, D'Antoni wanted to assure Stoudemire that he believes he is a terrific player and that he's 100 percent behind the Knicks' push to bring him to New York, sources said.
Stoudemire has told those close to him that much of the tension between the two was his fault, citing his youth and immaturity when he entered the league fresh out of high school. Stoudemire has said he's matured to the point that he now realizes D'Antoni was only trying to make him a better player, according to sources.
While the Knicks have not presented Stoudemire with a formal offer, they have discussed and pitched a five-year, $100 million deal, the maximum allowable under the league's collective bargaining agreement, according to sources.
The Knicks' plan is to get another top-flight free agent to play alongside Stoudemire, and the All-Star forward is all aboard for that plan. He's already tried to recruit LeBron James and Joe Johnson to join him in New York, though both players appear more likely to sign elsewhere.
But there is no shortage of players willing to team up with him in the Big Apple. Sources said that after Stoudemire arrived in New York on Saturday, he received calls from San Antonio's Tony Parker and Denver's Carmelo Anthony, saying they'd strongly consider joining him if he signs.
"I've talked to Carmelo Anthony that he needs to come out here," Stoudemire said on Saturday. "I've talked to Tony Parker. Both guys are ready to join me if I decide to come here. So we will see if we can work it out."
Parker and Anthony would not become free agents until next year. The Nuggets have offered Anthony a $65 million extension to remain in Denver through 2015.
Parker would have to get to New York via sign-and-trade and Anthony could sign as a free agent next offseason, provided he doesn't sign an extension with the Nuggets this summer and that the Knicks clear enough salary cap room.
Even if he can't get another free agent to play with him in New York this season, sources say Stoudemire is still willing to join the Knicks.
Chris Broussard covers the NBA for ESPN The Magazine.