Attorney John Tiemessen says the deadline for a decision is next week.
A state court judge ordered Miller pay more than $17,300 in legal costs incurred by the state during his challenge to the U.S. Senate race last fall.
Miller sued over how the state handled the election and counted votes for Sen. Lisa Murkowski, who ran as a write-in after losing her Republican primary to Miller.
In state court, winning parties can seek up to 20 percent of their attorney fees in cases where money wasn't at issue.
Three courts, including the Alaska Supreme Court, refused to overturn election results favoring Murkowski.
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