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.
Source: Red Sox get Castillo on 7-year deal
Kershaw dominates Padres, moves to 15-3
First-place Angels lose Richards 6-9 months
Tigers' Price tosses 1-hitter, but loses to Rays
Nationals up win streak to 10, walk off again
Angels complete 4-game sweep at Fenway
Olney: Trades worked for Angels, not for A's
Red Sox Invest In Cuban Outfielder Rusney Castillo
Jerry Crasnick discusses the Red Sox's seven-year deal with Rusney Castillo.
Nationals Walk Off Against Diamondbacks
Baseball Tonight Spotlight: Denard Span scored on a throwing error in the bottom of the ninth to lift the Nationals past the Diamondbacks 1-0, stretching Washington's winning streak to 10 games.
Kershaw Takes No-No Into Sixth
Clayton Kershaw surrendered his first hit in the sixth inning and struck out 10 over eight innings in the Dodgers' 2-1 win over the Padres.