It's no secret that New York Giants DE Osi Umenyiora has been unhappy with his current arrangement, but this does not sound like a situation that will quickly resolve itself. Seeing Osi (let's call him Osi!) being shopped around immediately after the end of the NFL lockout wouldn't be a surprise.
The Atlanta Falcons are believed to be in the market for a youngish veteran free agent pass rusher. Umenyiora has an injury history and 104 games worth of wear, but he's produced about .76 sacks per game in his career, including 11.5 in 2010. John Abraham had played only 73 games with the New York Jets before joining Atlanta, by comparison -- maybe the Falcons should just set up a pipeline for disgruntled New York defensive ends.
As Adam Schefter mentions above, Umenyiora recently moved full-time to Atlanta. He's often spent time training here, frequently being spotted working out with fellow NFL players at a swimming pool in Roswell. Of course, if the Falcons went and signed every player who moves to Atlanta, the team would have to just secede and start up its own league.
With Ray Edwards starting to look like a player the Minnesota Vikings will want to hang on to, the Meadowlands' loss could be the Georgia Dome's gain again, but I'd wonder whether there isn't a younger player who could provide a longer-term solution.