Smith, Fujita and Hargrove are expected to meet with Goodell on Tuesday.
Only Smith played on Sunday, when the Saints lost to Washington. Vilma was placed on the physically unable to perform list, while Fujita sat out Cleveland's loss to Philadelphia with a leg injury. Hargrove was cut by Green Bay during the preseason.
Players and coaches implicated in the bounty pool have testified under oath in a related federal court case they never intended to injure opposing players. The appeals panel ruled that Goodell could suspend the four players as long as the discipline was attributable to conduct detrimental to the NFL.
Around the league
Chargers • Running back Ryan Mathews has been cleared for contact but was limited in practice as the San Diego Chargers continued preparing for their home opener Sunday against the Tennessee Titans.
Mathews has been out since breaking his collarbone on his first carry in the exhibition opener Aug. 9. The Chargers don't have to list his status for the game until Friday.
Dolphins • Running back Daniel Thomas sat out practice for the second day in a row Thursday because of a concussion, increasing the likelihood Lamar Miller will make his NFL debut Sunday against Oakland.
Thomas, the backup to starter Reggie Bush, was hurt in the second quarter of Sunday's season-opening loss at Houston. Miller traveled with the team but was inactive.
Jets • The Jets will make a decision on cornerback Darrelle Revis availability before the team travels to Pittsburgh on Saturday for their game Sunday against the Steelers. Revis suffered a mild concussion in the season opener.
Week 2 schedule
Green Bay 23, Chicago 10
Tampa Bay at N.Y. Giants, 11 a.m.
New Orleans at Carolina, 11 a.m.
Arizona at New England, 11 a.m., Ch. 13
Minnesota at Indianapolis, 11 a.m.
Baltimore at Philadelphia, 11 a.m., Ch. 2
Kansas City at Buffalo, 11 a.m.
Cleveland at Cincinnati, 11 a.m.
Houston at Jacksonville, 11 a.m.
Oakland at Miami, 11 a.m.
Dallas at Seattle, 2:05 p.m.
Washington at St. Louis, 2:05 p.m.
Tennessee at San Diego, 2:25 p.m.
N.Y. Jets at Pittsburgh, 2:25 p.m., Ch. 2
Detroit at San Francisco, 6:20 p.m., Ch. 5
Denver at Atlanta, 6:30 p.m., ESPN