Treinen had a breakout season in 2018, authoring a 0.78 ERA over 80 1/3 innings while notching 38 saves to finish sixth in AL Cy Young voting. However, the right-hander lost the closer's gig in 2019, posting a 4.91 ERA.
A report surfaced last week suggesting the A's were looking to deal Treinen, along with Josh Phegley and Jurickson Profar, in order to shed salary. The club traded Profar ahead of Monday's non-waiver deadline, but it seems a deal never came to fruition involving Treinen.
Oakland also wound up non-tendering Phegley as well as left-hander Ryan Buchter.
Treinen, 31, was projected to earn $7.8 million in his final year of arbitration this year.
The New York Yankees were reportedly interested in acquiring Treinen.