Federal prosecutors in Manhattan are investigating whether President Trump’s 2017 inaugural committee misspent some of the record $107 million it raised from donations, people familiar with the matter said.

The criminal probe by the Manhattan U.S. attorney’s office, which is in its early stages, also is examining whether some of the committee’s top donors gave money in exchange for access to the incoming Trump administration, policy concessions or to influence official administration positions, some of the people said.

Giving money in exchange for political favors could run afoul of federal corruption laws. Diverting funds from the organization, which was registered as a nonprofit, could also violate federal law.

The investigation represents another potential legal threat to people who are or were in Mr. Trump’s orbit. Their business dealings and activities during and since the campaign have led to a number of indictments and guilty pleas. Many of the president’s biggest campaign backers were involved in the inaugural fund.

The investigation partly arises out of materials seized in the federal probe of former Trump lawyer Michael Cohen’s business dealings, according to people familiar with the matter.

In April raids of Mr. Cohen’s home, office and hotel room, Federal Bureau of Investigation agents obtained a recorded conversation between Mr. Cohen and Stephanie Winston Wolkoff, a former adviser to Melania Trump, who worked on the inaugural events. In the recording, Ms. Wolkoff expressed concern about how the inaugural committee was spending money, according to a person familiar with the Cohen investigation.

The Wall Street Journal couldn’t determine when the conversation between Mr. Cohen and Ms. Wolkoff took place, or why it was recorded. The recording is now in the hands of federal prosecutors in Manhattan, a person familiar with the matter said.

The inaugural committee hasn’t been asked for records or been contacted by prosecutors, according to a lawyer close to the matter, who said: “We are not aware of any evidence the investigation the Journal is reporting actually exists.”

The inaugural committee has publicly identified vendors accounting for $61 million of the $103 million it spent, and it hasn’t provided details on those expenses, according to tax filings. As a nonprofit organization, the fund is only required to make public its top five vendors.

The committee raised more than double what former President Barack Obama’s first inaugural fund reported raising in 2009, the previous record. President Trump’s funds came largely from wealthy donors and corporations who gave $1 million or more—including casino billionaire Sheldon Adelson, AT&T Inc. and Boeing Co. , according to Federal Election Commission filings. There is no sign that those three donors are under investigation.

Federal prosecutors have asked Richard Gates, a former campaign aide who served as the inaugural committee’s deputy chairman, about the fund’s spending and its donors, according to people familiar with the matter. Mr. Gates has met with prosecutors from the Manhattan U.S. attorney’s office and the special counsel’s office.

Mr. Gates, who served as deputy in the inaugural fund, in February pleaded guilty to conspiracy against the U.S. involving foreign political consulting work unrelated to the campaign. The case was brought by Mr. Mueller’s office. Mr. Gates agreed to cooperate with the Justice Department in ongoing investigations.

The committee was headed by Thomas Barrack Jr., a real-estate developer and longtime friend of Mr. Trump. There is no sign the investigation is targeting Mr. Barrack, and he hasn’t been approached by investigators since he was interviewed by special counsel Robert Mueller’s office last year, according to a person familiar with the matter. Mr. Mueller’s investigators, who are probing Russian interference in the 2016 U.S. election, asked Mr. Barrack only a handful of questions about the inaugural fund, the person said.

Mr. Mueller has also probed whether any foreign money flowed to the inaugural fund, which is prohibited from accepting foreign funds. In August, the U.S. attorney’s office in Washington, on a referral from Mr. Mueller, obtained a guilty plea from a Washington consultant who admitted he used a U.S. citizen to serve as a “straw purchaser” so that a “prominent Ukraine oligarch” could attend the inauguration. The names were never disclosed.

Manhattan federal prosecutors in recent months asked Tennessee developer Franklin L. Haney for documents related to a $1 million donation he made to Mr. Trump’s inaugural committee in December 2016, according to a person familiar with the matter. Mr. Haney in early April hired Mr. Cohen, at the time serving as Mr. Trump’s personal lawyer, to help obtain a $5 billion loan from the Energy Department for a nuclear-power project, the Journal has previously reported. Mr. Haney was asked for documents related to his correspondence with members of the committee, meeting calendars and paperwork for the donation, the person said. A loan application by Mr. Haney’s company is still pending at the Energy Department.

A lawyer for Mr. Haney didn’t respond to requests for comment.

The White House didn’t respond to requests for comment on the investigation. A lawyer for Mr. Cohen didn’t respond to requests for comment.

Since pleading guilty to federal crimes in August, Mr. Cohen has been cooperating with federal prosecutors in Manhattan and the special counsel’s office. He was sentenced Wednesday to three years in prison.

According to the inaugural fund’s tax filings, the committee’s top-paid vendor was an event-production firm led by Ms. Wolkoff called WIS Media Partners. The company, which California corporate records show was formed 45 days before the inauguration, was paid $25.8 million, the largest sum paid to a vendor.

Ms. Wolkoff is a former unpaid adviser to Mrs. Trump who also helped produce the inaugural. Ms. Wolkoff and several partners were paid about $1.6 million of the $25.8 million, and the remainder went to subcontractors, a person familiar with Ms. Wolkoff’s work said.

It couldn’t be determined which expenses are the focus of scrutiny by federal prosecutors. The committee said in its tax documents that it spent $77 million on conferences, conventions and meetings, plus $4 million on ticketing, $9 million on travel, $4.5 million on salaries and wages, and other expenses. Mr. Barrack has said that an external audit was completed of the inaugural committee’s finances, but the organization has declined to make that audit available.

The January 2017 inaugural events included a celebration concert at the Lincoln Memorial, receptions, private meals and inaugural balls.

People involved in Mr. Trump’s inaugural have attributed some of the costs to the last-minute nature of the planning. Few expected Mr. Trump to win the 2016 election, leaving his camp scrambling to arrange events for the inaugural, with little time to bid for competitive contracts, they said.

Write to Rebecca Davis O’Brien at Rebecca.OBrien@wsj.com, Rebecca Ballhaus at Rebecca.Ballhaus@wsj.com and Aruna Viswanatha at Aruna.Viswanatha@wsj.com