The market for late-inning relievers has been developing since the Washington Nationals signed closer Rafael Soriano last week. Farnsworth is among the several free agents remaining with closing experience.
The right-hander spent the past two seasons with the Rays and appears to be interested in rejoining them for a third. He maintained an ERA of 4.00 over 34 appearances spanning 27 innings in 2012.
Farnsworth was the Rays' closer for part of the 2011 season, posting a 2.18 ERA with 8.0 strikeouts and 1.9 walks per nine innings over 63 appearances while registering 25 saves. He owns an ERA of 4.24 and 52 saves over 14 seasons at the major league level.
Beyond the Rays, the Milwaukee Brewers have also been tied to Farnsworth this offseason. Other teams that could potentially be interested in the 36-year-old are the Seattle Mariners, Toronto Blue Jays, Detroit Tigers and New York Mets.