Sangmu Phoenix is made up of professional players doing their mandatory two years of military service and several have been caught up in the K-League match-fixing probe.
The team's coach was arrested this week for allegedly accepting money from the parents of a player to keep quiet about their son's role in the corruption scandal.
"We're considering leaving Sangmu off the K-League next season," an official from the military's athletics division told Yonhap news agency on Wednesday.
"But we're not looking into forcing Sangmu to stop accepting professional athletes altogether."
South Korea's government has already threatened to shut down the 16-team league unless it cleans up its act.
The K-League took a cautious approach to Sangmu's future, saying: "We're not yet at a point where we have to come up with [such punitive] measures."
The most damaging crisis to hit the professional K-League since it was launched in 1983 deepened last week when 46 players were arrested in relation to the attempted fixing of 15 matches from June to October last year.
Prosecutors have also charged 11 brokers, including several former players, with match-fixing, while 10 players have been slapped with life bans.
Nine of the players indicted last week were from Sangmu, surpassing the Daejon Citizen's previous ignominious high of eight, and they had to play a defender in goal in their 3-2 defeat by FC Seoul at the weekend as their regular goalkeepers were either arrested or suspended.
South Korean international Choi Sung-kuk has already confessed to being involved in match-fixing under a K-League amnesty in return for lighter punishment while in May a player was found dead in a hotel room, with media reporting a suicide note was found at the scene linking him with a betting ring.
