Robert Herzog, James Oldham and Dan Brent are expected to issue a decision Thursday, a day after listening to arguments.
Alvarez, 28, hit .231 with 18 homers and 56 RBIs last year, his poorest season since 2011. He has made 79 errors at third base during the last three seasons, and the Pirates plan to shift him to first.
Taken by the Pirates with the second overall pick in the 2008 amateur draft, Alvarez made $4.25 million last year. He is eligible for free agency after the 2016 season.