Greaves was reassigned to AHL Cleveland on Monday.
Greaves was called up by Columbus on Wednesday.
Greaves was sent down to AHL Cleveland on Saturday, according to Aaron Portzline of The Athletic.
Greaves will start on the road versus the Blues in Tuesday's preseason game, Matthew DeFranks of the St. Louis Post-Dispatch reports.
Greaves will defend the road net in Monday's preseason matchup against the Sabres, according to Joe Yerdon of Bleacher Report.
Greaves signed a two-year, $1.625 million contract with the Blue Jackets on Friday, Elliotte Friedman of Sportsnet reports.
Greaves will patrol the home crease versus Carolina in Tuesday's season finale, Jeff Svoboda of the Blue Jackets' official site reports.
Greaves will get a road start Saturday versus the Predators, Jeff Svoboda of the Blue Jackets' official site reports.
Greaves turned aside 42 shots in Thursday's 4-0 loss to the Panthers.
Greaves is expected to start on the road against Florida on Thursday, per Jeff Svoboda of the Blue Jackets' official site.