Covington was on the Bengals' roster to start the season before being waived on September 10. He played in three games for Cincinnati in 1999, completing four-of-five passes for 23 yards.
Covington could see action as early as Sunday's game at Baltimore.
Jon Kitna has been bothered by a sprained middle finger on his throwing hand and did not start in Sunday's 15-14 loss to the New York Jets. Akili Smith started in his place and suffered a torn hamstring that will sideline him for the season.
Backup Scott Mitchell, another possibility to start this week, strained his rib cage in practice.
In another move, the Bengals placed cornerback Mark Roman on the injured reserve list.
Roman dislocated the middle finger on his right hand in practice Wednesday. A second-year player from Louisiana State, Roman has started the last eight games and played in each contest this season. He has collected an interception and a fumble, and has broken up seven passes.
The Bengals (4-9) have lost six straight games.
Notable deaths of 2014 [PHOTOS]