The Diamondbacks acquired Alcantara from the Pirates on Tuesday in exchange for cash considerations.
The Pirates reassigned Skenes to minor-league camp Sunday.
Alcantara signed a minor-league contract with the Pirates on Dec. 9.
Alcantara signed a minor-league contract with the Diamondbacks on Aug. 1 and has gone 2-for-18 with a home run, three walks, four runs and four RBI in five games for Triple-A Reno.
Alcantara was reassigned Thursday to the minor-league side of Cubs camp, Paul Sullivan of the Chicago Tribune reports.
Alcantara went 2-for-3 with a double, a run scored and three RBI in Tuesday's Cactus League game against the Rangers. He also stole his first base of the spring.
Alcantara signed a minor-league deal with the Cubs on Tuesday.
Alcantara will start at third base and bat seventh in Monday's game against the Brewers.
Alcantara hit a walkoff three-run home run in his only at-bat during Wednesday's 5-3 victory versus the Dodgers.