The AL West champion A's rallied around Neshek after his newborn son, Gehrig, died 23 hours after his birth just before the playoffs began last month. Oakland players took the field wearing patches in the baby's honor during their five-game division series loss to the Detroit Tigers.
He went 2-1 with a 1.37 ERA in 24 appearances with the A's after being acquired from Baltimore on Aug. 3 for cash considerations. Neshek, who made $825,000 last year, was 3-2 with 11 saves and a 2.66 ERA in 35 Triple-A appearances before joining Oakland.
He can earn an additional $75,000 in performance bonuses: $25,000 each for 45, 55 and 65 games.
The remaining six A's players eligible for arbitration are first baseman Daric Barton, reliever Jerry Blevins, catcher George Kottaras, first baseman Brandon Moss, infielder Adam Rosales and designated hitter/outfielder Seth Smith.