The Predators placed Foudy on waivers Thursday, according to Nick Kieser of Nashville Hockey Now.
Foudy registered his third point of the season with an assist in Saturday's 4-3 loss to the Rangers.
The Predators claimed Foudy off waivers from Columbus on Saturday, according to Elliotte Friedman of Sportsnet.
The Blue Jackets have designated Foudy a non-roster player and placed him on waivers Friday and will assign him to AHL Cleveland should no team claim him, Jeff Svoboda of the Blue Jackets' official site reports.
Foudy scored a goal on four shots in Tuesday's 4-3 loss to the Flyers in overtime.
Foudy scored a goal and an assist in Tuesday's 5-4 overtime loss to the Penguins.
Foudy hasn't recorded a point in 16 straight NHL games, including Tuesday's 4-0 loss to the Senators.
Foudy wasn't in the lineup for Friday's loss to the Islanders.
Foudy earned an assist in Friday's 6-3 loss to the Avalanche.
Foudy (shoulder) will suit up for Monday's preseason tilt with Carolina, Aaron Portzline of The Athletic reports.