David Marcus, Head of Calibra at Facebook, testifies about Facebook's proposed digital currency called Libra, during a Senate Banking, House and Urban Affairs Committee hearing on Capitol Hill in Washington, DC, July 16, 2019.

Facebook said on Tuesday that Switzerland's data protection agency will oversee data and privacy protections for its new cryptocurrency, Libra.

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.