The A's picked up the options on left-hander Brett Anderson and center fielder Coco Crisp while deciding against keeping catcher Kurt Suzuki and outfielder Chris Young, the club announced Friday.
Suzuki and Young are now free agents.
Anderson's option is for $8 million and Crisp's is for $7.5 million.
Anderson, whose injuries forced him into the bullpen in 2013, is one of six starting pitchers on the A's roster, along with Jarrod Parker, A.J. Griffin, Tommy Milone, Dan Straily and Sonny Gray. The team also is looking at bringing back Bartolo Colon, who is a free agent. Anderson and Milone are the only left-handers in the group.
If the A's decided to trade one of their starters, Anderson is perhaps the most likely to be dealt. His name has been linked in trade talks with Toronto.
Crisp might get the contract extension he has been hoping to receive. The 33-year-old became a 20-homer, 20-steals man for the first time in his career in 2013.
Yankees: Shortstop Derek Jeter, 39, agreed to a $12 million, one-year deal that replaces a $9.5 million player option.
Jeter was limited to 17 games this past season after breaking his ankle in the 2012 playoffs. He spent four stints on the disabled list in the most frustrating season of his 19-year career.
Rangers: Closer Joe Nathan, 38, is a free agent after declining a $9 million contract option.
Nathan, who had indicated he wants a multiyear deal, had 80 saves over the past two seasons in Texas.
Red Sox: Boston picked up the $13 million option on left-hander Jon Lester.
Mets: Left-hander Johan Santana is a free agent after New York declined a $25 million option.
Indians: Right-hander Ubaldo Jimenez became a free agent after declining an $8 million option.
Pirates: Left-hander Wandy Rodriguez exercised his $13 million player option.
The Associated Press contributed to this report.