Perhaps the Jets won’t have to take up Jamal Adams’ offer to play cornerback.

Desperate for depth at their weakest position, the Jets on Tuesday signed Marcus Cooper. The 29-year-old veteran was released by the Lions on Monday having played four games for Detroit last season.

Cooper has also spent time with the Bears, Cardinals and Chiefs, and in 74 career games (28 starts) has tallied seven interceptions, one touchdown and two forced fumbles.

The Jets lost Kyron Brown to a hamstring injury Monday, a day after he replaced Trumaine Johnson, who is also suffering from a hamstring injury.

That prompted the Pro Bowl safety Adams to tell reporters he’d play corner if needed.

Also on Tuesday the Jets released tight end Nick Truesdell, who was fighting for playing time with starter Chris Herndon serving a four-game suspension for violating the NFL’s substance abuse policy.