The two met for about 90 minutes at Loria's Manhattan office, just a few hours after Girardi and the Yankees returned from Anaheim on Thursday morning. The Marlins asked for and received permission to speak with Girardi about the job on Wednesday.
According to Girardi, he and Loria plan to meet again, possibly next week, with Marlins general manager Larry Beinfest joining the discussions.
"It was fairly brief; he didn't want to do too much without Beinfest there. We talked about getting together again," said Girardi, who was joined by his agent, Steve Mandell. "The idea that he wants to talk to me is a good sign. It means I still have a chance."
"He's as intelligent as anybody; knowing and self-assured," said Yankees manager Joe Torre. "He's very well prepared, for the managing job and for what we have the rest of the way here."
Girardi is in his first season as the Yankees' bench coach, having spent the 2004 season as a broadcaster for the YES Network after his 2003 retirement.
After returning from the West Coast around 8:30 a.m. ET on Thursday, Girardi remained in the Yankees' clubhouse for about three hours, studying up on the Marlins' organization.
"You look over their club, the contracts, the prospects in the system, and see how it all fits," Girardi said. "It sounds like [pitcher A.J.] Burnett will be gone, so there are holes. The interest is, how are those holes going to be filled?"
Girardi and Loria aren't strangers, as Loria used to be a Yankees season-ticket holder, sitting in the front row on the first-base side.
"He saw me a lot when he came to the park, because I was always backing up first base," joked Girardi. "He makes you feel pretty comfortable."
Girardi said that none of the other teams with vacant managing jobs have contacted the Yankees for permission to interview him, though the Devil Rays are believed to be interested in the 40-year-old former catcher.
Girardi believes that he will be an aggressive manager, keeping the focus on defense and pitching. Having played in both the American and National Leagues, he feels he has a good grasp of today's players.
Girardi plans on speaking with Al Leiter, who played for the Marlins during the first half of the season before being traded to the Yankees in July.
"I'll talk to him, but I don't want to take away from anyone's focus," Girardi said. "The most important thing is to win tonight."
For Girardi, the Marlins job would represent a tremendous opportunity, given that many first-time managers are forced to take over clubs after 100-loss seasons. Florida was in the Wild Card race until the final week, so it's not hard to believe that the Marlins could contend right away under their next manager.
"They have some very talented young players," Girardi said. "You look at [Josh] Beckett and [Dontrelle] Willis, those two stand out; they have [Miguel] Cabrera in left field, who is probably as good a hitter as anyone in baseball. So your 1-2 starters are filled and you have your three-hole hitter, so you try to build around that.
"They have some talent, for sure. And they have more coming."
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.