Loomis and Vitt were at the league offices Thursday morning, with coach Sean Payton to arrive later in the day for his appeal.
Goodell suspended Payton for all of next season for his role in the bounty system. Loomis was suspended for eight games and Vitt for six. The Saints were fined $500,000 and docked two second-round draft picks.
NFL investigators concluded that from 2009-11 the Saints offered improper cash bonuses for big hits that either knocked opponents out of games or left them needing help off the field.
