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.
Yanks' Tanaka makes start, gives up homer
Jobe, pioneer of Tommy John surgery, dies
Phillies' Hamels to rest arm another week
Manny, not ready to retire, hoping to get call
Parnell, Niese, Colon face hitters in Mets camp
Red Sox reliever Hill says infant son has died
Karabell: Do not draft Kemp or Kimbrel
Yankees Hold Off Phillies
Masahiro Tanaka allows a home run in his first spring start with the Yankees, a 4-3 win over the Phillies.
Puig, Dodgers Throw Out Trout
Mike Trout gets tagged out at home plate trying to complete an inside-the-park home run.
Should Pujols Be Angry With Trout Comparison?
Michelle Beadle, Marcellus Wiley and Max Kellerman debate whether Albert Pujols should be upset about being asked if he was motivated to put up the same numbers as Mike Trout.