Pressure is growing for federal regulators to hold Facebook CEO Mark Zuckerberg personally accountable for his company's string of privacy scandals.

The Federal Trade Commission (FTC) is wrapping up a long-running investigation into Facebook over its data practices and is expected to levy a multibillion-dollar fine. But a report from The New York Times said that a rift has opened at the agency over whether to also hold executives like Zuckerberg liable in any enforcement action.

Last month, Facebook told investors that it's expecting to pay a fine as high as $5 billion to settle the FTC's investigation into its privacy practices. That sort of sum would be the largest fine ever leveled against a tech company in the U.S. — more than 200 times the record $22.5 million penalty Google received in 2012 for allegedly deceiving users about its privacy practices.

Still, the fine itself would be minuscule for a behemoth like Facebook, which last year made $55 billion in revenue. Investors largely shrugged off the expected fine, sending Facebook's stock up 10 percent the day after the announcement.

Facebook's critics say that the fine would amount to a slap on the wrist and that in order to hold the company accountable after a string of privacy incidents, the FTC needs to impose restrictions on its handling of user data and make executives individually liable.

That approach also has supporters in both parties.

"As important as remedies on Facebook as a company are, the FTC should impose tough accountability measures and penalties for individual executives and management responsible for violations of the consent order and for privacy failures," Sens. Richard Blumenthal (D-Conn.) and Josh Hawley (R-Mo.) wrote in a letter to the FTC on Monday.