Davidsson won't receive a qualifying offer from Ottawa, which means he'll become an unrestricted free agent Monday, Bruce Garrioch of the Ottawa Sun reports.
The Senators have loaned Davidsson to Vasterviks IK of Sweden's Hockey Allsvenskan league.
Davidsson was demoted to AHL Belleville on Sunday.
Ottawa recalled Davidsson from AHL Belleville on Friday.
Davidsson was traded from the Blue Jackets to the Senators along with Vitali Abramov, a first-round pick and a conditional first-round pick in exchange for Matt Duchene and Julius Bergman, Bob McKenzie of TSN reports.