By NICK TIMIRAOS And JEAN EAGLESHAM

The investigation by the Securities and Exchange Commission into Fannie Mae and Freddie Mac is homing in on the extent to which the mortgage-finance giants adequately disclosed their exposure to subprime loans, according to people familiar with the investigation.

The agency on Friday sent a Wells notice to Daniel Mudd, the former chief executive of Fannie Mae. A Wells notice indicates that the SEC staff is preparing to recommend civil enforcement actions and gives individuals the opportunity to persuade regulators against such an action.

Similar notifications have been sent to at least two other officials who worked with Mr. Mudd at Fannie, according to people familiar with the matter. One current Freddie Mac executive and the company’s former chief financial officer disclosed last month that they had received Wells notices.

News of potential civil charges against Mr. Mudd was reported earlier by Bloomberg News. Mr. Mudd is the highest-ranking official to have disclosed receiving such scrutiny in the investigation. He said in a statement that he plans to submit a written response to the SEC.

The agency is weighing whether to include charges against Fannie Mae and Freddie Mac—in addition to individuals—in any enforcement action, according to people familiar with the matter. They said the decision was complicated by the fact that any penalties would in effect be a charge on the American taxpayer.

The federal government took control of Fannie and Freddie in 2008 as rising loan losses wiped out thin capital levels.

Mr. Mudd has been chief executive since 2009 of Fortress Investment Group LLC, the New York-based hedge fund. One person close to the situation indicated that Mr. Mudd has the full support of the board and principals of Fortress.

The agency’s investigation into the conduct of the two mortgage giants in the run-up to the financial crisis is wide-ranging, according to people familiar with the matter.

But one of the key issues being looked at by SEC officials is the public disclosure by the two institutions of their exposure to subprime mortgages, including the extent to which possible losses were reported in a timely manner.

Fannie and Freddie typically defined subprime loan purchases as those either identified by the originator as subprime or those purchased from subprime originators.

Some critics say those metrics understated the firms’ exposure to subprime loans, particularly as loan standards deteriorated at the peak of the housing boom.

According to the statement from Mr. Mudd, the disclosures under investigation by the SEC were “accurate and complete,” had been previewed by federal regulators and “have been issued in the same form since the company went into government conservatorship.” Mr. Mudd declined to elaborate.

Mr. Mudd took the helm of Fannie in 2004 in the midst of an accounting scandal and oversaw its financial-reporting restatement with the SEC. He was sacked by the government when it took control of the firm in 2008. In August 2009, he became CEO of Fortress.

Printed in The Wall Street Journal, page A4