(Reuters) -Concerns about financial market stability, including the potential for a sharp drop in asset prices, are emerging as a fresh theme for Federal Reserve officials as they debate when and even whether to cut interest rates further. 

In a talk at Georgetown University on Thursday, Federal Reserve Governor Lisa Cook did not offer a view on near-term interest-rate policy specifically.

But she called out a range of risks to the financial system,  including fast-growing private credit markets, hedge fund trading in the Treasury securities market, and the adoption of generative artificial intelligence into machine-based trading.

Cook also suggested she would not be surprised by a collapse in historically elevated asset prices - which have helped shore up overall consumer spending and the U.S. economy more broadly - though such a decline would not by itself signal financial market instability.  "Currently, my impression is that there is an increased likelihood of outsized asset price declines." 

Speaking at a separate event earlier, Cleveland Fed President Beth Hammack reiterated her opposition to further interest-rate cuts because inflation remains too high, and signaled she sees easy financial conditions as another argument against rate cutting. 

While cutting rates might be framed as "taking out insurance" for the job market, she said, "we should be mindful that such insurance could come at the cost of heightened financial stability risks." 

She, like Cook, said she feels that the financial system is in good shape,  with banks well-capitalized and households holding solid balance sheets. But also like Cook, Hammack said she is watching elevated leverage levels in hedge funds, and feels that private credit merits watching.

The pair's remarks echo some of the concerns of Fed policymakers more broadly, as highlighted in minutes of the Fed's October meeting published on Wednesday. 

"Some participants commented on stretched asset valuations in financial markets, with several of these participants highlighting the possibility of a disorderly fall in equity prices, especially in the event of an abrupt reassessment of the possibilities of AI-related technology," the minutes said. 

The debate among policymakers has largely centered on whether another rate cut could let inflation that has been running above the Fed's 2% goal for years move even further in the wrong direction, or if the more pressing concern is a cooling labor market that requires more Fed policy easing.

The decision over what to do at the Fed's upcoming December 9-10 meeting has been further complicated by a government shutdown that has deprived policymakers of critical data to take the economy's pulse.

The Bureau of Labor Statistics on Thursday reported that September job gains were more than twice what economists had expected, even as the unemployment rate ticked up to 4.4%; the agency will not publish another comprehensive employment situation report until the week after the Fed's December meeting. 

After the economic data traders stuck to their previous bets that without data showing a decisive collapse in the job market the Fed will most likely skip a rate cut in December before delivering another quarter-point cut in January.