This comes shortly after the news that the Saints have signed K Wil Lutz to a contract.
Finnegan, 32, is a former seventh round pick of the Titans back in 2006. He spent the first four years of his career with Tennessee before joining the Rams in 2012.
St. Louis cut him after two years and he later caught on with the Dolphins in March of last year. Miami ultimately cut Finnegan loose in a move that freed up $5.475 million in available cap space before the start of free agency last year.
The Panthers wound up signing him to a contract towards the end of last year. The Saints later signed Finnegan to a one-year contract close to a month ago.
In 2015, Finnegan appeared in five games for the Panthers and recorded 18 tackles, no interceptions and a pass defense. Pro Football Focus had him rated as the No. 51 cornerback out of 111 qualifying players.