Gonzalez told MLB.com he spoke with Marlins general manager Larry Beinfest on Thursday about the position in Florida.
"We're going to try to set up an interview either between series or on a day off," Gonzalez said.
The Braves are facing the Astros in the National League Division Series, with Game 2 at Turner Field on Thursday. While there is an off-day in the series on Friday in Houston, it is likely Gonzalez will interview for the Marlins position early next week.
The Marlins are in the hunt for a manager after Jack McKeon stepped down following the season finale on Sunday to accept a position as advisor to team owner Jeffrey Loria.
The Marlins finished tied for third place with the Mets in the NL East at 83-79.
On Wednesday, the Marlins contacted Braves general manager John Schuerholz, asking permission to interview Gonzalez. Permission was granted. On Monday, Gonzalez interviewed for the Pirates' managerial job.
Gonzalez has been the Braves' third-base coach the past three seasons. From 1999-2001, the Havana, Cuba, native was the Marlins' third-base coach. Gonzalez spent a number of years in the Marlins organization, managing in the team's Minor League system.
Gonzalez has extensive experience managing in the Minor Leagues, dating back to 1990. In 10 years as a Minor League manager, he has a 628-596 record.
Along with Gonzalez, the Marlins also were granted permission to interview Yankees bench coach Joe Girardi. And newspaper reports out of the Oakland area claim the Marlins have contacted A's third-base coach Ron Washington, who is expected to interview on Tuesday.
There also is a belief the Marlins will interview Ken Macha, who will not return as manager of the A's.
Joe Frisaro is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.