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.
Yankees' Pineda banned 10 games by MLB
Yanks batter Red Sox with bounce-back barrage
Wrigley cake ends up down in the dumps
Tommy John stunned by surgery 'epidemic'
Sosa to 'clear it up,' sad to miss Cubs party
Nady's single in 12th lifts Padres over Nats
Crawford: Taveras now No. 1 hitting prospect
Padres Edge Nationals In 12
Baseball Tonight Spotlight: Xavier Nady's RBI single in the 12th lifted the Padres to a 4-3 win over the Nationals.
Pedro Gomez and Andrew Marchand break down Michael Pineda's 10-game suspension for having a foreign substance, which appeared to be pine tar, on his neck.
Yankees Pound Red Sox To Take Series
Jacoby Ellsbury and Derek Jeter combined for five RBIs in the Yankees' 14-5 win over the Red Sox.