Adolpho Birch, the NFL's senior vice president of labor policy and league affairs, sent a memo to the NFL Players Association warning that suspensions will go into effect on Aug. 26 if the players fail to cooperate.
A copy of Birch's letter to the NFLPA was obtained by USA Today and multiple media outlets. Any suspension will remain in effect until the player meets with league investigators and then Commissioner Roger Goodell will decide whether to lift any disciplinary action.
The players were among those linked to PEDs in a report by Al-Jazeera last year.
Five-time NFL Most Valuable Player Peyton Manning, who retired after guiding the Denver Broncos to a Super Bowl championship in February, also was named in the report. The league announced last month that Manning had been cleared of any wrongdoing, noting he and his wife were "fully cooperative."
Birch in his letter to the union said that the league had made "at least seven attempts" to set up interview times with the four players, only to be continually rebuffed by their "refusal to participate."
The NFL also deemed the half-page statements submitted by the NFLPA on behalf of each player as a failure to meet the palyers' obligations and accused Neal of making a statement that is "demonstrably false."
Matthews, a six-time Pro Bowl selection, has amassed 67.5 sacks in seven seasons with Green Bay.
A first-round draft pick out of the University of Southern California in 2009, he registered a career-high 13.5 sacks in 2010 en route to leading the Packers to a Super Bowl title.
Peppers, who is entering his 15th season and third with Green Bay, is ninth on the all-time list with 136 sacks.
Harrison earned NFL Defensive Player of the Year honors with the Pittsburgh Steelers in 2008, becoming the first undrafted player to win the award.
Harrison, who has spent all but one of his 13 seasons with the Steelers, had one of the most memorable plays in Super Bowl history, returning an interception 100 yards for a touchdown on the final play of the half in Super Bowl XLII.
Neal, another linebacker with the Packers, spent his first six seasons with Green Bay. He appeared in all 16 games in each of the past three seasons, starting 28, and has 19 career sacks.