Recently, Cook didn't get the franchise tag from the Titans and looks slated to become an unrestricted free agent over the next week. He's a high-impact pass catcher who has rare speed for a tight end.
Both head coach Rob Chudzinski and offensive coordinator Norv Turner have had success with receiving tight ends of late. Chudzinski utilized Greg Olsen to the latter's fullest potential in Carolina while Turner helped Antonio Gates become a premier weapon with the Chargers.
Cook has the potential to be a serious receiving threat wherever he goes and could conceivably be the Browns' number one option in the passing game if given the opportunity to succeed. Cleveland doesn't currently have any sure-handed wideouts on the roster and could use a player like Cook.
The main problem will exist under center, where the Browns still don't have any definite answer. Brandon Weeden looked overmatched in his rookie year and running back Trent Richardson even let on that the signal caller had a hard time reading defenses, which is a death sentence for any quarterback in the NFL.
Even if Cleveland brings in Cook, will they be able to get him the ball? Weeden has a solid arm when it comes to uncorking long passes, but he struggles throwing underneath and it's doubtful he'd be able to utilize Cook to the tight end's full potential.
That said, it seems as though the Browns want to build a solid enough offense around whoever is under center so that the onus won't be on the quarterback when the chips are down. This strategy usually doesn't work, but as recently as 2011 the 49ers got to the NFC Championship Game without leaning too much on Alex Smith.
If the Browns wanted to do this, they should consider giving Colt McCoy an opportunity to start over Weeden. McCoy turns the ball over much less and has great accuracy to the short part of the field.
However, in bringing in both Chudzinski and Turner, Cleveland was making a statement that they want to open up the passing game down the field. The two coaches are notorious for their good work with strong-armed quarterbacks like Cam Newton and Philip Rivers. Weeden could be their next project if they deem him fit to start.
An offense consisting of Weeden, Richardson and Josh Gordon all with a year of experience under their collective belt doesn't seem all that bad when adding a playmaker like Cook to the mix.
Cleveland could also look at outside linebacker Paul Kruger in free agency and may have to decide between Kruger and Cook if push comes to shove. Both would be big-name, break-the-bank signings and typically teams only make one of those moves per year.
The Browns' main competition in the Cook sweepstakes could come from the Chicago Bears, who also need a pass catching tight end.
For some statistical context, Cook caught 44 passes in 2012 for 523 yards and four touchdowns. He's a very fast tight end who would be an immediate upgrade at the position for Cleveland.
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