The Rangers inquired about Yoenis Cespedes more than once when he was a member of the Athletics, but they are unlikely to chase him in free agency.
Jeff Banister earned 17 first-place votes and 112 total points to beat A.J. Hinch (82 points) of the Astros and Paul Molitor (33) of the Twins.
The Rangers received right-handed reliever Tom Wilhelmsen, outfielder James Jones and a player to be named, while Seattle also obtained right-handed reliever Anthony Bass.
Mike Maddux, who spent seven seasons with the Rangers, had been among six coaches invited to return and was previously offered a new contract that he had not signed.