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.
Rangers Sweep A's
The Rangers beat the A's 7-2 for their sixth straight win.
Washington: Not True To My Wife
Former Texas Rangers manager Ron Washington issued a statement saying he resigned after he was not true to my wife.
Angels Win AL West
The Angels clinched the AL West title with a 5-0 win over the Mariners and the Athletics' loss to the Rangers.