But Facebook hasn't reached out to the Swiss regulator, a spokesman for the agency told CNBC.
In his testimony before the Senate Banking Committee on Tuesday, David Marcus, the head of Facebook's digital currency project, said, "For the purposes of data and privacy protections, the Swiss Federal Data Protection and Information Commissioner (FDPIC) will be the Libra Association's privacy regulator."
Asked about the agency's role regulating Libra, Hugo Wyler, head of communication at the FDPIC, said in a statement to CNBC:
"We have taken note of the statements made by David Marcus, Chief of Calibra, on our potential role as data protection supervisory authority in the Libra context. Until today we have not been contacted by the promoters of Libra," Wyler said. "We expect Facebook or its promoters to provide us with concrete information when the time comes. Only then will we be able to examine the extent to which our legal advisory and supervisory competence is given. In any case, we are following the development of the project in the public debate."
A Facebook spokesperson confirmed that the company hasn't yet met with the FDPIC.
Facebook's cryptocurrency project has already been met with skepticism from policymakers around the world. U.S. Treasury Secretary Steven Mnuchin and Federal Reserve Chairman Jerome Powell both said they have "serious concerns" about Libra related to money laundering, financial stability and regulation. Many of the senators who questioned Marcus on Tuesday also brought up data privacy concerns tied to Libra.
While FDPIC would handle data privacy issues, the Swiss Financial Markets Supervisory Authority, or FINMA, would be the main financial regulator of Libra, Marcus said in his testimony. FINMA confirmed to CNBC it was in contact with initiators of the Libra project.