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.
Verlander (triceps) plays catch, feels 'better'
Ex-LB Magee uses Bo's advice with Red Sox
M's prospect dies 6 weeks after boat accident
Rockies' Gonzalez pain-free after knee scare
Teixeira bruises knee on HBP, says he's fine
Indians choose McAllister, House for rotation
Olney: 5 teams that answered questions
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