Espinosa was hitting .162 with just 14 extra-base hits and 19 RBI in 77 games for the Angels this season, with his woes exacerbating team-wide struggles to generate offense.
The Angels rank third-to-last among American League teams in runs and batting average, and have scored four runs in two games since returning from the All-Star break despite getting two-time MVP Mike Trout back from a thumb injury.
If Espinosa is released, the Angels would be responsible for the rest of his $5,425,000 salary.
While Angels manager Mike Scioscia appreciated Espinosa's defensive presence, the offensive production was lacking.
"I think Danny brought some good things that helped us, but the offensive side, obviously, the struggles were obvious," Scioscia said.
"At that position we definitely need more of an offensive input. You would have to be really deep to absorb the lack of offensive production."
Espinosa, who spent the first seven seasons of his career with the Washington Nationals, was acquired by the Angels in a trade last December.