The website Politico reported that when Cain was head of the National Restaurant Association, at least two women complained of sexually suggestive behavior.
Both women reportedly left the association with five-figure payouts and agreed not to talk about it. Neither woman was identified.
The National Restaurant Association refused to comment on a personnel matter.
Cain, the former pizza company executive, has been pointing to his long record in business to argue that he has the credentials needed to be president during a time of economic strife.
A new poll shows Cain is leading former Massachusetts Gov. Mitt Romney by one point in Iowa, even though Cain has spent almost no time campaigning in the state.
Congressman Ron Paul is a distant third. Every other Republican candidate is polling in single digits.
The Associated Press contributed to this report.