Cambridge Analytica (CA), hired by the Trump campaign in the 2016 US election, has been accused of taking the personal data unknown to users.
CA head Alexander Nix has now been suspended by the company board.
The move came amid allegations the firm may have broken US electoral law.
CA, which is based in London, denies any wrongdoing.
Meanwhile, Facebook’s stock has continued to slide, following a steep decline on Monday.
The British and European parliaments have called on Facebook boss Mark Zuckerberg to give evidence to them., and the social network is due to brief congressional aides on Wednesday.
Mr Zuckerberg did not attend a Facebook staff briefing on the crisis at its Californian headquarters on Tuesday, which was led by deputy general counsel Paul Grewal instead, the Daily Beast news site reports.
The FTC is an independent agency of the US government tasked with protecting American consumers.
It is investigating whether Facebook violated the terms of a 2011 decree regarding the social network’s privacy protections, an unnamed source “familiar with the agency’s thinking and not authorised to speak on the record” told the Washington Post newspaper.
This was confirmed by a Bloomberg news agency report, quoting an unnamed “person familiar with the matter”.
Under the 2011 decree, Facebook must notify users and obtain their permission before data about them is shared beyond the privacy settings they have established, the Washington Post says. Facebook was also subjected to 20 years of privacy checkups to ensure compliance.
Facebook confirmed on Tuesday that it was expecting to receive a letter from the FTC with questions about the data acquired by CA. However, it also said it had had no indication of a formal investigation, Reuters news agency reports.
“We remain strongly committed to protecting people’s information,” Facebook deputy chief privacy officer Rob Sherman said. “We appreciate the opportunity to answer questions the FTC may have.”
In its statement on Tuesday, it said: “The entire company is outraged we were deceived. We are committed to vigorously enforcing our policies to protect people’s information and will take whatever steps are required to see that this happens.”
Christopher Wylie, who worked with the consultancy firm, alleges that it amassed large amounts of data through a personality quiz on Facebook called This is Your Digital Life.
He says that 270,000 people took the quiz but the data of some 50 million users, mainly in the US, was harvested without their explicit consent via their friend networks.
Mr Wylie says that data was sold to CA, which then used it to psychologically profile people and deliver pro-Trump material to them, with a view to influencing the outcome of the 2016 election.
CA insists it followed the correct procedures in obtaining and using data – but it was suspended from Facebook last week. (Courtesy BBC)