After the head of Calibra at Facebook, David Marcus testified on Tuesday's Senate hearing that Swiss data protection agency Federal Data Protection and Information Commissioner (FDPIC) will oversee the cryptocurrency's privacy protection, the regulator said the social media giant has not been in contact yet.

In a statement sent to CNBC, FDPIC Head of Communication, Hugo Wyler, clarified that it acknowledges Marcus' statements regarding its role in regulating Libra. However, Facebook has yet to discuss the details. "Until today we have not been contacted by the promoters of Libra," Wyler revealed.

Wyler further explained that Switzerland's privacy protection group is expecting Calibra leaders to provide "concrete information" about the highly-contested cryptocurrency. He stressed that the regulator can only determine the extent of its role after Facebook provides the necessary information regarding the Calibra project.

Marcus did clarify on Tuesday's hearing that Switzerland's Financial Markets Supervisory Authority (FINMA) will still be the main overseer of Libra activities. The office confirmed that it has been communicating with the Calibra heads.

The proposed cryptocurrency has been under fire over the past few weeks as the U.S. Federal Reserve and other American lawmakers expressed data privacy concerns and activities that could lead to money laundering.

During the hearing, the U.S. Senate grilled Marcus as he tried to explain the good side of Facebook's proposed cryptocurrency. It appears that most senators rejected the supposed benefits the new digital money will bring.

"Like a toddler who's gotten his hands on a book of matches," top Democrat on the Senate Banking Committee, Sherrod Brown, said of the Calibra project, CBS News reported.

Furthermore, the U.S. Senate refused to buy Marcus' pledge that the Calibra team will take its time in ensuring that the cryptocurrency will not breach user privacy laws and break the trust of lawmakers if this trust is given.

It's not just Brown who had doubts about the privacy regulations Libra will be controlled with. Republican Sen. Martha McSally said the people of Arizona "will be more likely to be scammed" when they use the digital currency since they will be forced to provide personal information to use Libra.

Marcus vowed that Facebook will not have special privileges since it is just among the many other companies under the Libra Association that can use the digital wallet if it is approved.

It is unclear how much Facebook invested into the massive Calibra project that continues to be under the watchful eye of the Fed, the Senate, and other global privacy regulators. Analysts noted that they were surprised of how much knowledge the Senate gleaned about Libra before the hearing, indicating that further questioning could be on the table.