Horwits said Rhodes narrowed his interest down to three teams, but would not disclose the other two clubs besides Cincinnati. The clubs that are out are starting to be notified. No details about the offers were disclosed.
Finding a veteran left-handed reliever has been a priority for Cincinnati at the Winter Meetings. General manager Walt Jocketty has also had talks with free agent Dennys Reyes and has shown interest in Joe Beimel.
Last season for the Mariners and Marlins, the 39-year-old Rhodes was 4-1 with a 2.04 ERA in 61 games. After a July 31 trade to Florida, he posted a 0.68 ERA in 25 games.
Overall, lefties batted .157 (11-for-70) against Rhodes, while right-handers batted .309 (17-for-55). Over his 17-year big league career, lefties have batted .221 against Rhodes while right-handers have hit .245.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.