While declining to discuss the teams, Rodriguez said, "Some teams are calling ... You'll find out pretty soon."
The new possibilities, Minnesota and San Francisco, were identified by a source with a National League team in the bidding.
The Twins' interest may depend on the health of star catcher Joe Mauer, who's had a back issue early in camp. The Giants have Bengie Molina to catch, and he's even penciled in as their cleanup hitter, but Pudge could get games at first base and third base in San Francisco, which is planning to employ youngsters Travis Ishikawa and Pablo Sandoval at those positions, respectively.
The Marlins play only 15 minutes from Rodriguez's home, but they also like their young catcher, John Baker. The Astros' catchers are struggling this spring, but they haven't been very aggressive so far in their pursuit of Pudge, who's played superbly for Puerto Rico in the World Baseball Classic, hitting .545 with two home runs.
"I'm in tremendous shape and still believe I can play on an everyday basis," said Rodriguez, whose Puerto Rico team plays the United States Saturday night here in a marquee second-round matchup. "Whatever happened last year unfortunately happened in a free agent year. But last year's over, and I'm focused on putting a good year together. I'm ready to play every day, and if the opportunity comes to play every day, I will do a good job. I care about baseball, and I'm a winner. I'm feeling good, and I still have a lot of baseball left in me"