Galvis is expected to sign with the NPB's Fukuoka SoftBank Hawks, Yahoo Japan reports.
Galvis went 1-for-4 with a solo home run in a 5-4 loss to the Marlins on Sunday.
Galvis isn't starting Thursday's game against Atlanta.
Galvis isn't in the lineup for Wednesday's game against Atlanta, Matt Breen of The Philadelphia Inquirer reports.
Galvis will sit Saturday against the Pirates.
Galvis is starting at third base and batting sixth Friday against the Mets, marking his fourth start in the past five games.
Galvis went 3-for-4 with a two-run home run in Wednesday's win over the Cubs.
Galvis is out of the lineup for Wednesday's game against the Brewers.
Galvis went 1-for-3 with a two-run home run, an additional run scored and a walk in Sunday's win over the Marlins.
Galvis (quadriceps) was reinstated from the injured list Tuesday.