The Hill publication cited law enforcement officials as saying Thursday that at least one witness was questioned last month and additional actions were expected in the coming weeks.
Hillary Clinton, who served as the top US diplomat between 2009 and 2013, is suspected of having traded political favors for lavish contributions to the foundation.
Federal Bureau of Investigation (FBI) investigators, who took the lead in the probe, will also look at whether tax exemptions were abused for personal or political reasons, the outlet said.