The Bengals are pretty much done with free agency in terms of anyone that will cost more than a veteran-minimum deal.
That includes receiver/returner Brandon Tate and backup quarterback Jason Campbell. Geoff Hobson still thinks the Bengals could re-sign those two, along with special-teams ace Cedric Peerman.
I think they’re still looking at re-signing backup quarterback Jason Campbell, as well as running back and special teams co-captain Cedric Peerman, and, quite possibly wide receiver/returner Brandon Tate.
The Bengals also reportedly want Peerman signed before April, so we could see some movement there this week. As for Tate, the Bengals may wait to re-sign him until after the draft to see if they can't get a returner there.
Another player who could sign with a team this week is outside linebacker Brandon Copeland. The Bengals previously met with Copeland at the NFL Veterans Combine, and he apparently visited Cincinnati, per Hobson:
The Bengals are looking for backers and Copeland is on their radar. He’s a 260-pounder undrafted out of Penn in 2013 who has knocked around some practice squads. He’s visited and maybe they’ll sign him.
Copeland has previous NFL experience with the Baltimore Ravens and Tennessee Titans before joining the Arena Football League's Orlando Predators. Few players ever make it from the Arena league to the NFL, but it looks like someone is going to give Copeland the chance to make the move.