Albert Breer of Sports Illustrated reported that the substance wasn't "immediately recognizable" and is being analyzed.
Breer declared that the test came in the offseason "a couple months ago." That rules out stimulants, which are included in the substances of abuse policy, separate from the performance-enhancing policy.
Edelman, who is appealing his suspension, did not acknowledge violating the league's policy on performance-enhancing substances in the posting on his Instagram account last week.
"I am very sorry -- I don't know what happened," Edelman wrote on the posting. "I've taken many, many tests obviously over the course of my career, and nothing like this has ever happened. I apologize to the Kraft family, my coaches, teammates and fans.
"As this matter is being appealed, I can't say anymore but no matter what, I will be ready to play and pursue another championship with our team and for Patriots fans around the world."
Edelman missed the entire 2017 season after suffering a torn ACL in an exhibition contest in August.
The 32-year-old Edelman trains with Alex Guerrero, who defended his methods in a statement on Thursday night.
"I've known Julian since his rookie year and he is a phenomenal athlete who takes his training seriously -- it's disappointing to hear today's news," Guerrero said. "Elite athletes sometimes work with multiple coaches and health professionals as part of their training.
"Here at our facility, we take a natural, holistic, appropriate and, above all, legal approach to training and recovery for all of our clients. And anyone who would suggest otherwise is irresponsible, and just plain wrong."
Edelman has been a favorite target of Patriots quarterback Tom Brady when healthy over the last several seasons. He caught 98 passes for a career-high 1,106 yards in 2016.
A converted college quarterback who was a seventh-round draft pick of New England in 2009, Edelman has recorded 425 receptions for 4,540 yards and 24 touchdowns in 103 career games.
New England added Jordan Matthews and Cordarrelle Patterson this offseason and selected Braxton Berrios in the sixth round of the 2018 NFL Draft to join a depth chart that includes Chris Hogan, Phillip Dorsett, Malcolm Mitchell and Kenny Britt.
Mitchell, like Edelman, missed the entire 2017 season and has been limited to conditioning drills during the team's offseason program.