Shares were down more than 2% following the news. The report says employees at the company are concerned that the emails could come under scrutiny during an investigation from the Federal Trade Commission.
The FTC is investigating whether security lapses related to the Cambridge Analytica scandal violated a 2012 consent decree between the agency and Facebook, according to the report.
The emails, which were described to the Journal reporters but not seen, reportedly show that Zuckerberg raised questions about how the company was sharing data with third-party developers, suggesting he knew of potential problems.
In an e-mailed statement, a Facebook spokesperson said, "We have fully cooperated with the FTC's investigation to date and provided tens of thousands of documents, emails and files. We are continuing to work with them and hope to bring this matter to an appropriate resolution. Facebook and its executives, including Mark, at all times strive to comply with all applicable law, and at no point did Mark or any other Facebook employee knowingly violate the company's obligations under the FTC consent order."