The Federal Trade Commission is considering taking sworn testimony from Facebook Inc. Chief Executive Mark Zuckerberg and Chief Operating Officer Sheryl Sandberg as part of its investigation into whether the social-media giant has violated U.S. antitrust laws, according to people familiar with the matter.

Top Facebook officials are preparing for potential depositions and some are worried about the possibility, a person familiar with the matter said. However, the company now is most immediately planning for Mr. Zuckerberg’s…

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