The Hungarian midfielder spent two-and-a-half years in the Potteries.
City have always believed they are entitled to cash under FIFA rules and have now made their case at the highest level.
Chief executive Tony Scholes said: "Our legal advice has been that, at the very least, we have a very strong case.
"We wanted Adam to stay here and offered him a new contract when he was still 18, but he decided to sign for Brescia where he has since played at least 100 games.
"We have been unable to agree anything with Brescia and so have taken this through the various levels at FIFA to the Court of Arbritation."
Source: Team Talk
Source: Team Talk