Allen was designated for assignment by the Athletics on Monday.
Allen spent time on the COVID-19 injured list in mid-April, but he saw sporadic playing time when healthy. Over five games, the 28-year-old went just 1-for-14 with a run, a walk and nine strikeouts. He'll now lose his spot on the 40-man roster, and Christian Bethancourt is in line to serve as the No. 2 catcher while Stephen Vogt (knee) is on the IL.