Eiftert was a Pro Bowler in 2015 when he caught 52 passes for 615 yards and 13 touchdowns, but it was in that game he first hurt his ankle.
He has 127 catches for 1,537 yards and 20 scores as a pro.
So far this offseason, the Bengals have acquired offensive tackle Cordy Glenn from the Bills and signed offensive lineman Bobby Hart and defensive lineman Chris Baker while declining to pick up a contract option for cornerback Adam Jones.
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They have also seen quarterback AJ McCarron, defensive lineman Chris Smith and offensive lineman Andre Smith sign elsewhere.
Earlier in the day, the team announced it has re-signed punter Kevin Huber.