WASHINGTON — Facebook and the Federal Trade Commission are discussing a settlement over privacy violations that could amount to a record, multibillion-dollar fine, according to three people with knowledge of the talks.

The company and the F.T.C.’s consumer protection and enforcement staff have been in negotiations over a financial penalty for claims that Facebook violated a 2011 privacy consent decree with the agency, said the people, who spoke on the condition of anonymity because the investigation is private.

In 2011, Facebook promised a series of measures to protect user privacy after an investigation found it had harmed consumers with its handling of user data.

The current talks have not yet reached the F.T.C.’s five commissioners for a vote and it is unclear how close the two sides are to wrapping up the nearly 11-month investigation. The commissioners met in mid-December and were updated by staff members that they had at that point found considerable evidence of violations of the 2011 consent decree.