Adam Schefter and Field Yates of ESPN reported the news Friday and noted the ban is in the appeal process.
Edelman missed the entire 2017 season after suffering a torn ACL during the preseason.
The 32-year-old Kent State product said Tuesday his rehab has been "good" and said the recovery is "one of those things where each step you take, you're prepared for that step."
"Any time you get to go out and see the fellas, play with them, talk with them, be in the huddle and look at guys, and participate in drills, that's what you play the game for ultimately," he told reporters. "It was tough to watch it on the sidelines last year. To come out here and do little things, strap on the helmet, it put some perspective on how lucky you are to get to play the game."
Edelman made 98 catches for 1,106 yards and three touchdowns while playing all 16 games in 2016. He's tallied 425 receptions for 4,540 yards and 24 scores since the Pats selected the converted quarterback in the seventh round of the 2009 draft.
The California native is also one of the New England players to showcase his work with Alex Guerrero, the personal trainer of quarterback Tom Brady.
In December, Bob Hohler of the Boston Globe reported Patriots head coach Bill Belichick "stripped Guerrero of his special team privileges," meaning he could no longer travel on the team jet, be on the sideline during games or treat players other than Brady at Gillette Stadium.
If the suspension is upheld, Edelman would miss games against the Houston Texans, Jacksonville Jaguars, Detroit Lions and Miami Dolphins. He'd be eligible to return for the team's Week 5 clash with the Indianapolis Colts.