Any settlement will also be looked at as a measure of the Trump administration’s willingness to penalize one of the country’s most valuable and influential companies. The administration has whittled away regulations in many industries, but President Trump has repeatedly said tech giants like Facebook and Amazon have too much power.

Many Democrats have led efforts to rein in Silicon Valley’s power.

“This is a hugely important decision because it will be watched by all these big companies to see if there is actually going to be a new day on the enforcement front,” said Senator Ron Wyden, an Oregon Democrat who has pushed for Mr. Zuckerberg to be held personally liable in any settlement.

Rohit Chopra, one of the two Democrats on the commission, has publicly urged stronger punishment of repeated offenders of F.T.C. rules.

But Mr. Simons has appeared unwilling to force the issue and drag the case to court, which could be a risky move. He has recently intensified his efforts to get at least one of the two Democrats on his side, according to one of the people with knowledge of the talks. But the internal disagreements have held up a final agreement.

In addition to the fine, Facebook has agreed, as part of a proposed settlement, to create new positions that would be focused on privacy policies and compliance, two of the people said. The agency, in coordination with the company, would set up an independent committee to oversee Facebook’s privacy efforts. That committee and the F.T.C. would appoint an outside assessor to monitor the company’s handling of data.

The company has also agreed to assign an executive as a privacy compliance officer, making privacy oversight a job within the top ranks, the people said. Mr. Zuckerberg could be given the job, according to one person with knowledge of the talks, although another person expressed doubts.