The situation seemed to come to a critical mass on Wednesday at the NFL owners meetings, when the story was first reported, but the end result will likely have Mathis staying with the Eagles for at least the 2014 season.
The team views Mathis as a very good guard in their system and would be more than willing to pay him his $5.15 million base salary. But some teams have been lukewarm about him because of his age and because he's not considered a traditional mauler or a scheme fit, two NFL general managers said.
The Eagles also like backup guard Allen Barbre and would be comfortable sliding him into the starting spot if Mathis were to be traded, a source close to the situation said.
Eagles coach Chip Kelly said that Mathis had not conveyed to him that he wanted a new deal. Factoring in signing bonuses, Mathis was the 14th highest-paid guard in the NFL before the start of free agency.
"I think that's just the nature of what our league is like," Kelly said about Mathis' contract demands. "In professional sports, there is a short amount of time that guys have to play this game, and they're trying to get what they can, and I certainly understand where they're coming from."
When the Eagles signed him off the street in August 2011, after six journeyman NFL seasons, it was for one year and approximately $700,000. Mathis wound up winning a starting job in camp, started in 15 games, and was lauded by veteran offensive line coach Howard Mudd for his Pro Bowl-level of play.
Mathis re-signed with the Eagles as a free agent the following offseason and was the only offensive lineman to start all 16 games. While he didn't earn Pro Bowl or all-pro nods, his blocking was lauded by such player-rating websites as Pro Football Focus.
Mathis didn't miss a snap in 2013 and was once again arguably the Eagles' most consistent linemen. He earned both first-team all-pro and Pro Bowl honors, but his salary remains a notch below the highest-paid guards. The Buccaneers' Carl Nicks ($7 million), the Saints' Jahri Evans ($6.8 million), and the Titans' Andy Levitre ($6.5 million) have the highest 2014 base salaries.
"Evan has been since Day 1, since I got here, just outstanding," Kelly said, "whether it's in the meeting rooms, in the weight room, on the practice field - he practices every day."
As well as he's played in two different offenses the past three years, there is some feeling around the league that he isn't big enough at 6-foot-5 and 298 pounds to excel in a system that doesn't require its linemen to block as much in space.
The Eagles extended the contracts of two other offensive linemen this offseason. Left tackle Jason Peters received a four-year, $41 million extension, with around $19 million guaranteed. Center Jason Kelce got a six-year, $37.5 million contract with $13 million guaranteed.