The Jets lost tight end Dustin Keller to Miami earlier in free-agency, and Jeff Cumberland will not be a capable replacement.
Davis missed nine games last season with an Achilles injury and has had a streaky career with the Redskins.
After catching 48 passes for 500 yards and six touchdowns in 2009, Davis had only 21 receptions and three touchdowns in 2010. Davis rebounded with 59 catches and almost 800 yards in 2011, but only caught 24 balls in seven games last season.
Despite his inconsistencies throughout his career, Davis believes he is about to have a huge year.
In an interview with "NFL AM," Davis explains his self-confidence, "And I’ll bet you next year’s gonna be a good year for me. This is the one right here. This is the big one."
Davis also said during the interview that he would make every team that didn't sign him regret it.
The market for Davis has not been demanding, which could give the Jets a chance at signing him for a reasonable price. The Jets, Bills and Redskins are the only teams that have shown interest in Davis.
Davis is a player who has proven he can be a weapon on offense when healthy. A player with a chip on his shoulder is exactly what the Jets need right now.
If Davis' production can outweigh his injury history and off-the-field problems (he was suspended in 2011 after testing positive for marijuana), he could be a steal for John Idzik and could give the Jets a weapon they desperately need.