NFL Network's Mike Garafolo first reported the news.
NFL Network's Ian Rapoport added that the 38-year-old veteran still wants to play and will likely land a good contract on the open market because of the lack of quality offensive tackles available.
Garafolo noted that Peters and the Eagles, who have spent the past 11 seasons together, will remain in contact even as Peters tests the market.
Peters is a nine-time Pro Bowler and two-time First-Team All-Pro who has put together a resume that may be Hall of Fame worthy. Few could have expected that when he entered the NFL as an undrafted free agent with the Buffalo Bills in 2004 and converted from tight end to offensive tackle.
He was named a Pro Bowler in his final two seasons with the Bills and parlayed that into a huge contract with the Eagles, and he has been in Philly ever since.
Peters was part of the Eagles' Super Bowl-winning team three years ago, although he played in only seven regular-season games because of injury and did not appear in a playoff contest.
Injuries have been an issue for Peters in recent years, as he has missed games in two of the past three seasons, including nine in 2017 and three last season.
Halapoulivaati Vaitai has often filled in for Peters when he has been injured over the past few years, but he is set to hit free agency as well. Even so, the Eagles have a strong contingency plan in place.
Lane Johnson is locked in as the starting right tackle, and the Eagles selected Andre Dillard with the No. 22 overall pick in the 2019 NFL draft out of Washington State. Dillard appeared in 16 games and made four starts last season, and he will likely be Philly's new starting left tackle if Peters leaves via free agency.
Even as he inches closer to 40 years of age, Peters is still an effective player when healthy, so he could still be a useful piece of the puzzle somewhere in the NFL even if the Eagles decide to move forward with a younger option.