The Eagles are also expected to sign free-agent wide receiver Jeremy Maclin to a new deal, most likely a one-year, "show me" contract after he tore his anterior cruciate ligament last July. But talks between the Eagles and Cooper's representatives picked up over the last few days, and the 26-year-old receiver likely will be signed first.
While the Eagles had signed only the 32-year-old Peters by Wednesday, general manager Howie Roseman gave a clear indication that the Eagles were planning to reward some of their own players before free agency starts.
"We're going to try to keep - obviously it takes two to tango - our best players and the guys that we feel are part of our culture and that fit well into the chemistry of our football team on and off the field," Roseman said after Peters' news conference at the NovaCare Complex. "It's an important message for us this offseason. When you look at it, and everybody's talking about free agency, we know these players. We've lived with them. We've been married to them.
"I've talked a lot about arranged marriages in free agency. These aren't arranged marriages. We know how they work. We know how they act."
Cooper was embroiled in controversy last August when video surfaced of his using a racial slur. But the Eagles stuck by their 2010 fifth-round draft pick, and he avoided further incidents the rest of the season.
Filling in for the injured Maclin, Cooper caught 47 passes for 835 yards and eight touchdowns in 2013. He had great success with quarterback Nick Foles after Foles replaced Michael Vick, catching 39 passes for 742 yards and seven scores in the final 11 games of the season.
The 6-foot-3, 222-pound Cooper was arguably the Eagles' best downfield blocker. He was also their big-play threat - even more than fellow receiver DeSean Jackson - and averaged 17.8 yards per catch, third best in the NFL.
Roseman wouldn't confirm that the Eagles were in negotiations with Kelce, but he and coach Chip Kelly have made it no secret that they hope to have the 26-year-old center around for some time.
"Without getting into any specifics," Roseman said, Kelce is "a guy we drafted, a guy we think very highly of, and . . . a guy that really kind of fits that culture and the chemistry."
Kelce, like Peters before his new contract, is entering the final year of his deal. He has spoken freely about wanting to stay in Philadelphia beyond 2014. And Roseman said that the Eagles wanted to keep intact an offensive line that didn't miss a start last season.
Peters and guards Evan Mathis and Todd Herremans and tackle Lane Johnson - the latter three signed through 2016 - are under contract for the foreseeable future.
And Kelce will join them soon. Like Peters, he successfully returned from a major leg injury (a torn ACL) in 2013. Unlike Peters, he didn't make the Pro Bowl, although the argument could be made that he deserved to be selected.
Maclin remains a priority, but a deal has to be struck. He has said that he would accept a one-year contract and likely welcomes one, because it would be a quicker route to the long-term deal he ultimately wants.
Other teams are expected to be interested in the 25-year old, including the New York Jets, according to a New York Daily News report. But Maclin, who has spent the offseason rehabbing at the NovaCare Complex, may not reach free agency.
Aside from Cooper and Maclin, punter Donnie Jones is the most likely unrestricted free agent to remain with the Eagles.