Puerto Rico plays Team USA on Saturday at 8 p.m. ET in the second round of the World Baseball Classic at Dolphin Stadium.
The 37-year-old Rodriguez is off to a terrific start in the Classic. He was named the MVP of Pool D, which was played in Puerto Rico.
The Marlins and Mets have expressed interest in the veteran, and the Twins and Giants have been mentioned as possibly having interest in Rodriguez.
Rodriguez was a standout on Florida's 2003 World Series title team. The team has had discussions with Rodriguez's agent, Scott Boras. And the Marlins are closely monitoring the veteran's progress in the Classic.
"There have been some rumors that the Marlins have interest in me. As of now, there has been nothing firm yet," Rodriguez said. "Yes, there has been some communication between the Marlins organization and my agent."
Florida is ready to go with left-handed-hitting John Baker as its regular catcher, and playing time will be a factor in Rodriguez's decision. Considering the grind of the position, there are questions as to how many games whoever is the Marlins' primary catcher will play.
Florida believes Baker can handle 120 games, but he has 61 games of MLB experience.
The way Rodriguez has performed in the Classic has earned him the praises of his teammates and manager.
"He's one of the hardest workers on the team," said Bernie Williams, the former Yankees All-Star outfielder. "He's certainly committed to representing his country. I think this obviously has a has double motivation [for him]. It's a great showcase for him to display what kind of skill level he has. Hopefully he will open some eyes within baseball organizations and definitely let them know he can still play the game."
Puerto Rico's manager, Jose Oquendo, says Rodriguez would be an asset to a big league team, regardless of where he played in the field.
"I think Ivan is going to be ready to do whatever it takes to help a team -- be it behind the plate, be it first base, be it third base if he needs to," Oquendo said. "I think he's going to be willing to do that."
Rodriguez has appeared in 2,267 Major League games, and he's caught in 2,173 of them. In his 18-year big league career, he's been a designated hitter 52 times, and he's been at first base in seven games and second base once.
Rodriguez has a home in South Florida, and he would welcome returning to the organization where he won his lone title.
"It's been tough for me, to be honest with you," he said of waiting for a big league contract. "At the same time, the only control I have over myself is keeping myself in good shape. [I need to] keep working every morning and preparing myself, physically and mentally for any opportunities.
"I'm still looking for a job. It's hard for me and my family. I'm staying very positive. I know I'm going to have an opportunity, somewhere. We'll see if in the next few days something comes up."