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.
MLB marks 67th anniversary of Robinson debut
Napoli exits with hurt finger after headfirst slide
Rays P Moore needs season-ending surgery
CF Jones, RP Meek bitten by Orioles' flu bug
Astros prospect Springer: Headed to Houston
Pedroia gets cortisone shot in ailing wrist
Szymborski: Lester's real contract value
Reds Hold Off Pirates
Baseball Tonight Spotlight: Mike Leake struck out eight batters and hit a two-run home run to lead the Reds past the Pirates 7-5.
Athletics Top Angels In 11
Mike Trout tied the game with a two-run home in the ninth inning, but Josh Donaldson's RBI double in the 11th inning gave the Athletics a 10-9 win over the Angels.
White Sox Walk Off On Red Sox
Xander Bogaerts' throwing error led to Alexei Ramirez scoring the game-winning run as the White Sox defeated the Red Sox 2-1.