By Karen Freifeld

NEW YORK (Reuters) - A ruling by New York's highest court in a fraud case against former American International Group Inc <AIG.N> Chief Executive Maurice "Hank" Greenberg could affect the state's case against Republican presidential candidate Donald Trump and his defunct Trump University.

The New York Court of Appeals ruled on Thursday that state Attorney General Eric Schneiderman could seek to recoup millions of dollars in bonus payments to Greenberg using the legal remedy called disgorgement.

Unlike damages, which are used to compensate victims' losses, disgorgement requires a defendant to give back gains obtained from unlawful means. The ruling means that Schneiderman can go after $5 million he says Trump personally pocketed from the Trump University real-estate seminar venture.

"It doesn't help him," Jeffrey Goldman, Trump's lawyer in the New York case, said on Monday of the Greenberg ruling. But Goldman said Trump expected to win the case and could also try to limit the amount subject to disgorgement, such as by arguing that most of it was earned outside of New York.

According to the state's 2013 lawsuit against Trump, filed in state court in Manhattan, Trump University was an unlicensed, illegal operation that bilked students of up to $35,000 each between 2005 and 2011. Two proposed class actions in California make similar allegations.

Trump, the presumptive Republican presidential nominee, has repeatedly raised the Trump University litigation on the campaign trail, calling the lawsuits baseless and politically motivated. He has also accused the federal judge overseeing the California lawsuits of being biased against him because of his ethnicity. The judge was born in Indiana to Mexican parents.

In the Greenberg case, the state accused the former CEO of orchestrating sham transactions at AIG and misleading shareholders about the company's financial health between 2000 and 2005. Schneiderman is asking that Greenberg disgorge some $25 million in bonuses during that period, plus interest.

Greenberg has denied any wrongdoing. His lawyer, David Boies, who represented Democratic presidential candidate Al Gore in the dispute over the 2000 election recount, had argued that disgorgement was not a remedy available to the New York attorney general under either the state's securities fraud law or another fraud statute. The Court of Appeals rejected Boies' arguments.

The ability to seek disgorgement may be useful to Schneiderman because the California cases involving Trump University may be resolved before the New York case. One is scheduled for trial on Nov. 28, just a few weeks after the Nov. 8 election.

A settlement or judgment in those cases could undermine Schneiderman's claim for $40 million in damages because he is suing on behalf of many of the same former Trump University students. But disgorgement claims would not be affected.

(Reporting by Karen Freifeld; Editing by Anthony Lin and Peter Cooney)