The 28-year-old Denmark captain is one of many current and former players and staff of the Superliga club due a nominal fee after the club failed to pay supplementary holiday pay, pensions and benefits since 2004.
Agger told Liverpool's official website: "I am not going to claim any money from the club.
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Brondby were formed in 1964 and are the second-most successful club in Denmark with 10 league titles and nine Danish Cups to their name, but have fallen on hard times recently, finishing as low as ninth last year.
Agger believes they still hold an important place in Danish football though, adding: "Brondby are an important club, not just in football, but also for a lot of people in the local community.
"It is a huge organisation with a huge network. You can tell by the amount of people showing up to the games.
"I hope a lot of players will review their decision to claim the money. It won't be good for anyone if Brondby are not to be found in the best Danish division."