The 46-year-old Allen has overseen a Saints defense that transformed from one of the worst to one of the best in the league over the past two seasons.
The 68-year-old Capers was out of football last year after being fired by the Packers, though the early half of his nine-season stint in Green Bay included some strong units and a Super Bowl victory.
Both are also former head coaches.
Allen had a largely forgettable two-plus seasons with the Raiders, going 8-28 from 2012 until he was fired four games into the 2014 season.
Capers has been head coach of the Panthers and Texans when each came into the league as expansion teams.
The Cambridge, Ohio, native’s long coaching career also included a two-year stop (1980-81) at Ohio State, where he followed Nick Saban as defensive backs coach.
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A noteworthy aspect of the report: Allen and Capers run fairly different schemes.
Although both play a high-pressure style, Allen runs a 4-3 defense that relies on man coverage while Capers’ scheme is similar to the 3-4 zone-blitz defense Dick LeBeau developed in Cincinnati and perfected in Pittsburgh (where the two worked together).
The Bengals have been a 4-3 team for years and might need to rework the roster to effectively shift to a 3-4 scheme, though a talent upgrade is likely going to be necessary on that side of the ball either way.