La Canfora added the Browns are "very motivated" to move Haden's sizable contract entering the 2017 season.
The 28-year-old Haden has three out of five years remaining on his deal and will have a cap hit of $14.4 million in 2017, per Spotrac.
Haden is an elite-level corner when healthy, but the 2010 No. 7 overall pick out of Florida has struggled with injuries in recent years.
Haden was named to the Pro Bowl in both 2013 and 2014, registering seven interceptions and 40 passes defended in those two seasons combined.
Although he wasn't selected to the Pro Bowl in 2016, he enjoyed a fairly productive season for a struggling Browns team with 48 combined tackles, three picks and 11 pass breakups.
In seven NFL seasons, Haden has 19 interceptions.
Haden's rookie season in 2010 was the only year in which he has appeared in all 16 games, however, making him a potentially risky addition to any team that may have interest in him.
While Haden is a game-changer when healthy and playing to his potential, the Browns remain stuck in a lengthy rebuild, and possibly landing a quality draft pick may be of more value to them than the talented defensive back.