A signing would make sense for both parties. The Giants are trying to make a serious push to return to the playoffs and released ineffective starter Mathias Kiwanuka, and Graham is best suited for a 4-3 defense. Graham had a breakout season in 2014, tying a career high with 5.5 sacks, and was tied for fifth in the league with 4 forced fumbles, but did so playing in less than half of the Eagles' defensive snaps.
Earlier in the week, Graham and the Eagles were reportedly "[not] progressing very well", and there's been no news since then on any progress.
For more news and rumors on the Eagles free agent moves, check out our Eagles 2015 free agency rumor tracker.