The source told ESPNNewYork.com that Turner's propensity for not running hard irked the front office, which had finally seen enough.
Turner, arbitration-eligible, likely was due to make less than $1 million in 2014.
He should have no trouble finding a job this offseason. Among Turner's longtime fans is Atlanta Braves manager Fredi Gonzalez.
Giants fan gives historic HR ball to Ishikawa
Bumgarner, Shields get nods for WS opener
Sources: Red Sox near deal to hire Chili Davis
Sources: Dodgers ask Byrnes about GM job
Former Orioles, Yankees 2B Roberts retires
Rangers looking to extend GM Daniels' deal
Olney: Big questions loom for Orioles, Cards
Sources: Dodgers Ask Josh Byrnes About GM Job
ESPNLosAngeles.com's Mark Saxon explains new Dodgers president of baseball operations Andrew Friedman's interest in hiring former Diamondbacks and Padres GM Josh Byrnes.
Selig Swan Song
In his final season as commissioner of Major League Baseball, Bud Selig sits down with T.J. Quinn of "Outside The Lines" to discuss how he's handled his signature challenges during 22 years on the job.
Ishikawa: 'I Don't Remember Running The Bases'
Travis Ishikawa discusses his three-run walk-off home run to give the Giants a 6-3 win over the Cardinals in Game 5 of the NLCS.