It opens a 21-day window for the players to return to the roster.
The Saints placed Alonso on the physically unable to perform list Aug. 1 as he worked his way back from the ACL he tore in the playoffs. Montgomery has spent three weeks on injured reserve with a hamstring injury.
Alonso appeared in 13 games for the Saints last season, starting four, after they acquired him in a trade with the Dolphins. He made 31 tackles, three tackles for loss and two quarterback hits.
Montgomery signed with the Saints this offseason and had played two games before his injury.