Throughout the major leagues, shortstops are coming off the board – Juan Uribe to the Los Angeles Dodgers, Ryan Theriot to the St. Louis Cardinals.

And in recent days, sources say, the San Francisco Giants have become one of the most serious suitors for Tampa Bay shortstop Jason Bartlett.

San Francisco's interest picked up once Uribe signed with the Dodgers, a source said. Bartlett, 31, is the type of veteran player favored by Giants general manager Brian Sabean. He was born in Mountain View, Calif., and attended St. Mary's High School in Stockton, Calif.

The Rays need to rebuild their bullpen, and the Giants have enough depth there to move a reliever. San Francisco right-handers Chris Ray and Ramon Ramirez have experience in the American League East, but it’s not clear if the Rays have interest in them.

The Padres, Orioles and Pirates are also looking for a shortstop.

The Minnesota Twins aren’t negotiating an extension with their shortstop, J.J. Hardy, enhancing the odds he'll be moved. Hardy, 28, has more power potential than Bartlett, but Bartlett's the better small-ball player.

Bartlett's had a better OPS than Hardy over the past two seasons - .780, compared with .684.

-Jon Paul Morosi and Ken Rosenthal