In January, the Supreme Court upheld the High Court ruling that Parliament had to be consulted before Article 50 could be triggered.
Labour MP Gloria de Piero tabled a written question asking when the cost of the appeal would be published.
Brexit Minister Robin Walker replied: "The department has not been billed for all costs related to the case."
He continued: "Details of the total costs associated with the case, including the costs of the Supreme Court appeal, will be published in due course after they have been settled."
The government has rejected Freedom of Information requests for the cost to be revealed, saying it will be made public at a future date.
Investment manager Gina Miller and other campaigners won a case in the High Court last year against the government's assertion Article 50, the mechanism which kickstarts the process of leaving the EU, could be activated by royal prerogative.
Ministers appealed the decision in the Supreme Court and lost again.
They swiftly introduced the European Union (Notice of Withdrawal) Bill, which is currently making its way through Parliament.
If the bill is passed as expected next week, it will have taken longer to pay the legal bills for the appeal than to get MPs' and peers' approval to start the Brexit process.
The government has not yet finished paying the legal costs of its Supreme Court challenge over Brexit.