Greaves was loaned to AHL Cleveland on Wednesday.
Greaves will patrol the road crease Tuesday against Tampa Bay, according to Jeff Svoboda of the Blue Jackets' official site.
Greaves stopped 23 shots in Saturday's 4-3 overtime loss to the Ducks.
Greaves is in the starter's crease at morning skate, Mark Scheig of The Hockey Writers reports, and is expected to defend the home crease versus Anaheim on Saturday.
Greaves is expected to start in Thursday's home tilt against the Capitals, per Aaron Portzline of The Athletic on Wednesday.
Greaves was elevated from AHL Cleveland on Wednesday.
Greaves was reassigned to AHL Cleveland on Saturday.
Greaves was recalled by the Blue Jackets under emergency conditions Friday.
Greaves was reassigned to AHL Cleveland on Monday.
Greaves was called up by Columbus on Wednesday.