The right-handed Treinen posted a 0.78 ERA in 2018, but that number ballooned to 4.91 in 2019. He was replaced by Liam Hendriks in the closer role as the low-budget A's earned the American League's top wild card.
Treinen was expected to command roughly $7.5 million in arbitration.
Left-hander Ryan Buchter and catcher Josh Phegley also didn't receive contracts. Lefty T.J. McFarland reached agreement on a $1.8 million, one-year deal to avoid salary arbitration. He was claimed off waivers from the Diamondbacks on Nov. 4.
Treinen started the 2019 season as A's closer but wasn't nearly as consistent. He had a 6.14 ERA during a 19-game span from April 28 to June 20 before a strained pitching shoulder put him on the injured list. Once healthy and back July 3, Treinen didn't have a save over his next 27 appearances and posted a 6.17 ERA.
Oakland also said its other previously unsigned players were tendered contracts. That list includes the seven remaining arbitration eligible players: right-handers Chris Bassitt and Hendriks, outfielders Mark Canha, Robbie Grossman and Chad Pinder, lefty Sean Manaea and shortstop Marcus Semien.