"You've got four or five clubs maybe that figure to be in the sweepstakes. There aren't a lot of clubs that are going to be able to pay the money."
Torre walked away from the New York Yankees after 12 seasons as manager last month when they offered him a one-year contract with a paycut. Rodriguez also cut ties with the club, opting out of his $252 million, 10-year contract during Game 4 of the World Series and becoming the biggest prize on the free-agent market.
Now, some think the Dodgers could be a front-runner to land A-Rod, likely to win his third MVP award this month. Torre confirmed the two had a better relationship this season in New York.
"All I know is it was very comfortable for both of us," the manager said. "And I think my being uncomfortable came from the fact that I didn't think he was as comfortable. This year he just seemed to be a different guy in spring training."
Speaking before his Safe at Home Foundation's fifth annual gala, Torre said he was "surprised" Rodriguez opted out of his record deal to seek a new one.
"I really was. But you have to do what you think you need to do," he said.
Torre said he hasn't spoken with Rodriguez recently, but they've exchanged messages.
The Los Angeles Angels, New York Mets, San Francisco Giants and Boston Red Sox are other teams thought to be interested in Rodriguez. His agent, Scott Boras, asked the Yankees to make a $350 million offer just to get a meeting with A-Rod before he opted out of his deal.
The Yankees say they're out of the running.
The Dodgers are a big-market team - and they could certainly use a big bat. They hit only 129 home runs this season, ranking 15th out of 16 NL clubs, so the 32-year-old Rodriguez would be a perfect fit at third base. He batted .314 with a major league-best 54 homers and 156 RBIs this season, his fourth in New York.
Torre said owners Frank and Jamie McCourt are committed to making the Dodgers consistent winners again.
"All I can tell you, I know the McCourts are certainly dedicated to putting the Dodger franchise on the right track. They understand the pride factor. We talked about that a lot," Torre said. "But again, they're business people. They're certainly going to take into consideration what they can do that makes sense. And the fact that they have a lot of young players certainly could help make their decision, too."
Derek Jeter, Mariano Rivera, Jorge Posada and Bernie Williams were among Torre's former Yankees players who attended the event. Bruce Springsteen was on hand to provide entertainment.