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.
Sources: Padres keep dealing, get J. Upton
Yankees trade Prado to Miami, get P Eovaldi
Giants fill Sandoval hole, trade for McGehee
Report: Dodgers pass Yanks in owing most tax
Sources: Selig to earn $6M a year in retirement
Catcher Ross joining Lester with Cubs
Law: Norris deal is a win for both teams
Padres Complete Big Three With Upton Trade
Buster Olney discusses the excitement surrounding San Diego's new outfield after the Padres made deals to acquire Wil Myers, Matt Kemp and Justin Upton.
Jake Peavy Staying With Giants
Buster Olney reacts to the report that pitcher Jake Peavy and the Giants have agreed to a two-year, $24 million deal.
Yanks Bring Eovaldi To The Bronx
Andrew Marchand discusses how pitcher Nathan Eovaldi will fit into the Yankees' rotation.