Five teams - the St. Louis Cardinals, Los Angeles Dodgers, Milwaukee Brewers, Atlanta Braves, and Texas Rangers - are believed to be interested in acquiring the left-hander before the July 31 deadline, Jon Morosi of MLB.com reports.
The Cardinals and Giants had serious discussions about a potential deal during the offseason, sources told Morosi. St. Louis is poised to pursue the 30-year-old again as long as the team is still contending at the end of July, he adds.
Los Angeles is reportedly eyeing Smith in what could end up as a rare deal between the Dodgers and Giants. The two historic rivals haven't completed a trade since 2007.
The Braves and Rangers are looking to solidify the back end of their bullpens. Atlanta is currently using right-hander Luke Jackson (15 career saves) while Texas is turning to Shawn Kelley (26) in the 9th.
Should the Brewers land Smith, the team could pair him with fellow left-hander Josh Hader to create a devastating one-two punch late in games.
It was reported in late June that the Minnesota Twins were also interested in adding the veteran reliever.
Fresh off making his first All-Star appearance, Smith is poised to attract plenty of suitors with the Giants occupying last place in the National League West and reportedly in sell mode. He's perfect in save opportunities (23-for-23) heading into the second half with a sparkling 1.98 ERA and 53 strikeouts in 36 1/3 innings.