NFL Coaches' Association director David Cornwell said in an email to The Associated Press on Friday that he and Vitt had talked about the appeal. ProFootballTalk.com first reported Vitt's decision.
"Joe Vitt and I discussed our concern that his appeal be consistent with the association's view that coaches also coach sportsmanship and fair play," Cornwell said. "Based on these discussions, I am confident that Joe's appeal and his long history in the NFL are consistent with our belief that there is no place at any level of football for bounties that target players."
The NFL suspended Vitt, who also coaches linebackers, for the first six games of the season.
Earlier Friday, a person familiar with the decision told The Associated Press Sean Payton was appealing his season-long suspension.
Saints spokesman Greg Benson confirmed that Loomis was appealing his eight-game suspension and, separately, the team would challenge its $500,000 fine and loss of second-round draft picks this year and in 2013.
Former defensive coordinator Gregg Williams, who left the Saints after last season to join the St. Louis Rams, ran the bounty program and has been suspended indefinitely.