The team that is showing the most trade interest in Zobrist is the San Francisco Giants, according to Marc Topkin of the Tampa Bay Times. He adds that the Seattle Mariners and Cincinnati Reds are other teams that have shown interest.
Zobrist, 33, is a versatile defender which will intrigue a lot of teams. He mostly plays at second base and shortstop, but also has played left and right field this season with the Rays.
With the Giants, Zobrist would play second base, which is the position the Giants have been weakest at this season. They recently got Marco Scutaro back, but until he can prove to stay healthy, they are going to need to find someone they can count on day in and day out, and that's what Zobrist would provide.
No deal is imminent, but you can expect the Giants and many others to become more aggressive in their pursuit of Zobrist after the All-Star break.
In 82 games played this season, Zobrist is hitting .269 with six home runs and 24 RBI. He has a club option worth $7.5 million for 2015 that includes a $500,000 buyout.
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