Cullen Jenkins is a strong veteran presence and quality pass-rusher - for a defensive tackle.

When Jenkins is your starting defensive end - a position meant to be manned by sleeker, more dynamic pass-rushers, even on the left side in a 4-3 - you know there's something amiss.

For the New York Giants, Jenkins appeared in 12 games last season, starting 11. He finished with 15 total tackles and one sack. Again, he's a stand-up guy, but he's not the type of havoc-wreaking player you want manning a major quarterback sacking spot along your defensive line.

This is a fact apparently not lost on Giants GM Jerry Reese and head coach Tom Coughlin, as they have reportedly set their sights on former Philadelphia Eagles defensive end-turned-outside linebacker, Brandon Graham.

"According to sources Brandon Graham is leaning towards Dolphins and Titans but now the Giants may make him an offer he can't refuse," tweeted Derrick Gunn of CSN Philly.

It was reported yesterday, by Dan Graziano of ESPN, that the Giants were "still talking to" Graham.

While the Dolphins and Titans may have his ear for the time being, it seems that Reese and Coughlin are ready to up their offer to nab the pass-rush maven.

With Jenkins and Damontre Moore the main left defensive ends on the Giants roster, it's not hard to see why the New York brass is willing to pony up the dough for an ascending player like Graham whose speciality is getting to the quarterback

Pairing Graham - the most efficient pass-rusher in the league last year, per Pro Football Focus - with athletic marvel Jason Pierre-Paul would be a potentially dominant tandem.

Add in the fact that new Giants defensive coordinator Steve Spagnuolo loves to rotate his linemen and you could easily see how a player like Graham, raring and ready to rejoin a 4-3 and a guy who was thrived as part of a rotation, could be a nearly perfect fit in New York.