Cole completed his 10th season with the team in 2014. By releasing him this week, the team gives the veteran a head start on free agency, which begins next Tuesday at 4 p.m. ET.
"We spoke with Trent and his agent and expressed a desire to have him back," Eagles coach Chip Kelly said in a statement. "We have been talking for a couple of weeks. However, at this point, we think it's best to let him explore other options around the NFL."
Cole, who played eight seasons in a 4-3 defensive scheme, played his past two seasons with the Eagles in the 3-4. Because of his versatility, he should be an attractive free agent since so many teams play with hybrid defensive fronts.
Cole has 88.5 career sacks, second-most in Eagles history behind Reggie White, who had 124.
Cole, who was selected in the fifth round of the 2005 NFL draft by the Eagles, signed a four-year, $53 million contract extension with $14.5 million guaranteed in March 2012. He was the longest-tenured Eagle along with Todd Herremans, who was released last week.
ESPN Eagles reporter Phil Sheridan contributed to this report.