The team did not announce or explain the move, which is expected to be made after Galette passes a physical this weekend. He also has been recovering from a torn pectoral muscle.
Galette told The Times-Picayune the decision by the Saints is "the worst call they've ever made. It was a terrible call to kick me when I'm down".
The NFL has talked to Galette about his arrest in January for domestic simple battery, and the league is now investigating a 2013 video that purportedly shows Galette striking a woman with a belt during a scuffle in South Beach, Fla.
Galette, 27, was not charged in the domestic violence incident, which allegedly took place on Jan. 5 at his home in Kenner, La.
The beach video came to light last month, and the Saints forwarded it to the NFL.
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The Tampa Bay Buccaneers placed cornerback C.J. Wilson on the reserve/retired list.
Wilson lost two fingers in a fireworks accident on the Fourth of July.
Wilson, 25, had been slated to begin his second season with the Bucs. He appeared in two games for Tampa Bay in 2014, playing primarily on special teams and recording four tackles.
Wilson is in the final season of a two-year deal that carries a non-guaranteed base salary of $585,000 for the 2015 season.
The Buccaneers also waived linebacker Jared Koster, an undrafted rookie.
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Kansas City Chiefs cornerback Sean Smith was suspended for a violation of the NFL's substances of abuse policy.
Smith will miss three games stemming from his guilty plea to DUI charges in April.