His agent, Vince Taylor, told NFL Network's Mike Garafolo that Peters can earn up to $8 million this season.
Peters signed a one-year deal in August that would pay him $3 million guaranteed and could be worth up to $6 million. He was originally expected to play right guard after Brandon Brooks suffered a season-ending torn Achilles during a workout in June.
Starting left tackle Andre Dillard tore his biceps on Aug. 29, ending his season and leaving another hole on the offensive line.
Head coach Doug Pederson told reporters that Peters was in the discussion to take Dillard's spot.
Per Jeff McLane of the Philadelphia Inquirer, Peters wanted a raise that would pay him like a starting left tackle in order to play the more important position.
The 38-year-old has started 20 out of a possible 32 regular-season games since 2018 after tearing his ACL and MCL in Week 7 during the 2017 season.
Peters said in June 2017, upon receiving a one-year contract extension from the Eagles, his goal was to play for three more seasons through 2019 before walking away.
"I don't think I'm going to go that much longer," he told reporters. "Three-year extension. I'm going to give them everything I've got."
Reuben Frank of NBC Sports Philadelphia did note Peters is inching closer to becoming one of the few great players the Eagles have had over the past 30 years to end his career wearing green and white: "The best players, the most popular players, the most successful players, either had no desire to stay here when their contracts expired (thanks, Rich Kotite) or were unwanted and disposed of, left to finish their careers in anonymity in Cleveland, Jacksonville or Detroit."
Peters spent the first five years of his career with the Bills after signing as an undrafted free agent. He played tight end at the University of Arkansas and during his rookie season in Buffalo.
After learning to play offensive tackle during his second season, he has become one of the best players at the position. The Eagles acquired him prior to the start of the 2009 season, and he's gone on to start 140 games over the past 11 seasons.
Peters has been named to the Pro Bowl nine times and the All-Pro first team two times as a member of the Eagles (2011, 2013).
The Eagles are starting the season with a number of key injuries, especially on the offensive line, but having a rock like Peters back at left tackle should help make things easier for quarterback Carson Wentz.