The Marlins plan to interview Gonzalez perhaps as early next week to replace Jack McKeon.
On Monday, before the Braves began their National League Division Series with the Astros, Pirates general manager Dave Littlefield and assistant general manager Doug Strange flew to Atlanta to interview Gonzalez.
While Gonzalez came across impressively, the Pirates are believed to be leaning more towards former A's manager Ken Macha, a Pittsburgh native, and former Dodgers manager Jim Tracy.
On Thursday, the Marlins interviewed Yankees bench coach Joe Girardi at team owner Jeffrey Loria's offices in New York City. That session lasted about 90 minutes and a followup interview is being arranged.
Gonzalez, meanwhile, has the support of the Braves for a managerial opening.
"He's ready," Braves manager Bobby Cox said. "This is the right time to get him."
Gonzalez is no stranger to the Marlins organization, where he served as third base coach from 1999-2001. Born in Havana, Cuba, Gonzalez has about 10 years of experience managing in the Minor Leagues.
"He's a great communicator," Cox said. "He knows the game, inside and out. He's managed in winter ball and managed in the Minors. He has coached in the big leagues. Everybody has had to start sometime. We all had our first year. He's ready."
Braves general manager John Schuerholz, who granted the Marlins permission to interview Gonzalez, agrees.
The Braves, winners of a record 14 straight division titles, are regarded as the model franchise. The fact other teams are interested in their people isn't a surprise.
"It's more flattering for Fredi because it's a reflection of him and the esteem in which he's held," Schuerholz said. "It's nice to know that you've got guys like that who are a big part of your success that people are interested in. But it's really a reflection on him, the hard work he's done, and how he's grown in his stature in the game."
What Gonzalez brings to the table is simple, Schuerholz said.
"He knows the game," Schuerholz said. "He's very knowledgeable. He works hard at it. He communicates well with the players. He has a real feel for it. There are a certain people who have a natural kind of interactivity capability with players and other coaches, and he's one of them. He can do that."
That fact that Gonzalez speaks Spanish is certainly a plus on a Marlins squad that has a heavy Latin influence.
"He's learned a lot from Bobby Cox, and I think he can do it," said Braves MVP candidate Andruw Jones, who endorses Gonzalez. "I'll be happy for him. He's a good coach and he knows a lot. It will be good for him to get a chance to prove he can do it."