Arizona must be looking to bolster their pass-rushing depth ahead of their playoff game with the Packers on Saturday.
Babin, 35, signed a two-year, $3.25 million contract with the Jets back in July of 2013 and had his option picked up by the Jets last year. However, he wound up being among the team’s final roster cuts at the start of the season.
Baltimore signed Babin to a contract shortly after they lost OLB Terrell Suggs to season-ending Achilles injury.
This season, Babin has been active for just two games, but has yet to record a single statistic.
Shaughnessy, 29, was in the year of his final two-year, $4.4 million contract when he was among the Cardinals’ final roster cuts at the start of the season.
In 2014, Shaughnessy was limited to appearing in just eight games for the Cardinals after he was placed on short-term injured reserve. He finished the year with 17 tackles.