Girardi met with Marlins owner Jeffrey Loria for approximately 90 minutes on Thursday at Loria's Manhattan office. The two plan to meet again next week, along with Florida general manager Larry Beinfest.
It is unknown when Girardi may meet with the Devil Rays, who bought out the final year of Lou Piniella's contract in September.
"They've got a lot of talent -- and young talent," Girardi said of the Rays. "They've got a lot of speed; they've got some good young pitchers, players that are hungry. They haven't experienced the playoffs, a lot of those guys, and that makes players really hungry."
Girardi saw plenty of the Devil Rays this season, as Tampa Bay won 11 of its 19 meetings against New York during the regular season. The 40-year-old said he would definitely be interested in the job.
"They're a pain the neck to play against, I can tell you that," Girardi said. "I had to do a lot of little things to win, and they have to do a lot of them."
Yankees general manager Brian Cashman backed Girardi's candidacy for a managing job, whichever team he may end up with.
"He's a real quality baseball man; he's been a big asset for us this year as our bench coach," Cashman said. "I know he hasn't had any managerial experience, but he's managed the game behind the plate for so many years, and that, I think, makes up for a lot.
"I'm not surprised that anybody wants to call and talk to us about him, because he's a very good baseball person, without question."
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.
Should Girardi wind up with Tampa Bay, he would face an uphill challenge, to say the least. With 19 games each year against the Yankees and Red Sox, not to mention respectable teams in Toronto and Baltimore, the Rays would have their work cut out for them in order to escape the basement for just the second time in nine years.
"It would be great," Girardi said. "You're playing a great team every night."
Tampa Bay will interview coaches Tom Foley, Billy Hatcher and John McLaren and Triple-A Durham manager Bill Evers on Tuesday.
There is one more appealing thing about the Rays job for Girardi: Don Zimmer.
Zimmer, who coached or managed Girardi as a player in Chicago, Colorado and New York, is currently a senior advisor for the Devil Rays. Zimmer is signed for one more year, and Girardi said he would want the 74-year-old to be involved with the team.
"I'd want him around if I would be there," Girardi said.
Mark Feinsand is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.