Judge Thomas Wingate is expected to decide within seven days whether to dismiss the case or allow it to proceed to a forfeiture hearing.
Gov. Steve Beshear requested that the state pursue the seizure that was approved by a Kentucky circuit court judge last month.
According to a Washington Post report, the seized domains include gaming sites UltimateBet.com and FullTiltPoker.com. Gov. Beshear was elected on a platform that included bringing gambling to the state.
Several organizations have spoken at hearings about the seizure. According to the article, "trade groups, domain registrars and gambling advocates had an opportunity to tell Judge Wingate why the case should be dismissed outright."
Many organizations at the hearing requested an explanation of the legality of such an action, citing international law. Many online gambling sites are physically located outside of the United States.
A 2006 federal law prohibits U.S. banks from processing transactions that involve online gambling sites, but many U.S. citizens have found ways around the prohibition.