Federal prosecutors and casino company Las Vegas Sands Corp. have discussed settling a U.S. Justice Department probe into whether Sands violated money-laundering laws regarding a pair of high-rolling gamblers who were later charged with crimes, people familiar with the case said.

The two sides met as recently as Thursday. In July lawyers for the casino operator tried to persuade prosecutors to drop the case. Prosecutors countered that they could indict Las Vegas Sands on charges of conspiracy to commit money laundering and...