According to Pro Football Talk's Mike Florio, who was a guest on the Dan Patrick Show, via Fox Sports:
[The Patriots] need to work something out by next Tuesday. The problem is they couldn’t franchise [Welker] because it would cost them $11.4 million to keep him around. The ace in the hole for the Patriots is Danny Amendola.
It could be that the Patriots already have plans—and tampering’s not supposed to be happening—but every team is doing it. But they may already have an understanding that on the first day of free agency, they’re going to ink Danny Amendola to replace Wes Welker, which would make a lot of sense if that’s what they do.
The St. Louis Rams didn't use the franchise tag on Amendola, making him a free agent starting on March 9.
Signing him to a contract would certainly be far cheaper for New England than the one Welker will command. Amendola has spent more time on the IR than he has on the playing field the past couple of seasons with the Rams.
He dislocated his elbow and tore a triceps in the first game of the 2011 season—a season-ending injury. He then dislocated his clavicle in Week 5 of the 2012 season—a scary injury that could have been far more serious (h/t Fox Sports' Jay Glazer)—and missed five games while he healed.
That said, these two injuries don't automatically mean Amendola is injury prone. He played in 49 games during his college career at Texas Tech, and both of his injuries as a pro have been of the upper-body type.
Amendola's knees are fine, and he's going to be ready to rock and roll to begin the 2013 season.
Welker may end up signing a long-term contract with the Patriots. CSN New England's Tom Curran recently reported that the two sides "made progress" on a new deal.
We should take that news with a grain of salt though, after Yahoo! Sports' Jason Cole's revelation that a source close to Welker said he has "mild disdain" for New England, stemming from the first game of the 2012 season.
When healthy, Amendola has been undeniably productive. In his 42 career games as a pro (17 starts), the Welker clone has caught 196 passes for 1,726 yards and seven touchdowns. Additionally, Amendola returned punts and kicks for 3,710 yards in his four years with the Rams.
It's important to note that Amendola has been extremely productive while playing in a Rams offense that has been unable to protect its quarterback and has struggled to put up points.
Amendola would absolutely thrive in the slot with Brady slinging him the ball on a regular basis.
He'll be much cheaper to sign, and if Welker decides to test his worth on the market starting on March 9, then the Pats should have no qualms about signing Amendola in his stead.
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