WASHINGTON—A Treasury Department unit that specializes in combating money-laundering will share financial records with an expanding Senate probe into possible ties between Russia and President Donald Trump and his associates, according to people familiar with the matter.

The Senate Intelligence Committee requested the records from Treasury’s Financial Crimes Enforcement Network, or FinCEN, late last month, these people said. The people familiar with the matter didn’t specify the nature of those records. One person said that without them, though, the committee wouldn’t be able to reach a conclusion on whether there was collusion between Trump associates and Russia during last year’s campaign.

Sen. Ron Wyden (D., Ore.), a member of the intelligence committee and the ranking member of the Senate Finance Committee, said in an interview Friday that he is particularly interested in information about shell companies, money laundering and the use of property transfers that may be germane to the committee’s Trump investigation.

Representatives for FinCEN and Sens. Richard Burr (R., N.C.) and Mark Warner (D., Va.), the intelligence committee chairman and vice chairman, declined to comment.

Possible ties to Russia, which dogged Mr. Trump during the campaign and so far in his presidency, resurfaced as a major political issue this past week after Mr. Trump fired Federal Bureau of Investigation Director James Comey. Critics suggested that sudden move was an effort to interfere in the agency’s probe of potential Russian interference in the election, which both Moscow and Mr. Trump have dismissed. Mr. Trump has said he dismissed Mr. Comey because he wasn’t doing a good job.

On Capitol Hill, there is a separate House committee probe of alleged Russian interference to go along with the Senate investigation.

“We are confident that when these inquiries are complete, there will be no evidence to support any collusion between the campaign and Russia,” a White House spokesman said. Mr. Trump has repeatedly dismissed the FBI probe into the matter.

A former senior U.S. official indicated that federal investigators are examining whether Russian investments in any of Mr. Trump’s properties or business ventures could be traced back to Russian government sources, including Russian officials who might own banks that were lending money to Mr. Trump.

FinCEN receives hundreds of reports each day from financial institutions flagging suspicious activity, and it is tasked with making sure banks and other companies comply with rules to do so. It provides the data to law-enforcement agencies, and its own analysts examine the data to identify suspicious patterns of the flow of funds around the world. After the Sept. 11, 2001, terror attacks, for instance, the agency took the lead in tracking terrorist-financing sources and using financial records to help reveal the structure of terrorist networks.

On April 26, Messrs. Burr and Warner requested FinCEN provide the same records obtained by the FBI, which has its own access to the information, in its Russia probe.

The Senate intelligence panel’s request was made because investigators, who have been reviewing U.S. intelligence reports about Russian interference in the 2016 election, came across information that led them to inquire about Mr. Trump’s business ties, these people said. It marks an escalation for the committee’s probe from its original focus on intelligence reports that were used to conclude Russia had meddled in the 2016 elections, as well as documents the committee is seeking from some of Mr. Trump’s associates, including his former campaign manager, Paul Manafort, and his ex-national security adviser, Mike Flynn.

One person familiar with the Senate Intelligence Committee’s request for the records said investigators plan to look at Mr. Trump’s businesses, as well as companies that do business with him, and potentially a step beyond to companies that engage with those firms.

The inquiry could also include businesses owned by or associated with Mr. Trump’s family members, including Kushner Cos., where his son-in-law and now senior White House aide, Jared Kushner, was previously the CEO.

In 2015, FinCEN imposed a $10 million civil penalty against Trump Taj Mahal Casino Resort for “willful and repeated violations” of anti-money laundering requirements, according to an official statement at the time. The agency cited a prior history of violations dating back to 2003. In 1998, FinCEN assessed a nearly $500,000 penalty against Trump Taj Mahal for currently transaction reporting violations. Mr. Trump hadn’t owned or been involved with running the company since 2009.

On Friday, Mr. Trump’s lawyers released a two-month-old letter stating that 10 years of his tax returns—which he has refused to disclose—show he has little income, investments or debt from Russian sources, save those items already publicly known. The letter gave no indication that Mr. Trump plans to release his full tax returns.

But those tax records are unlikely to say much about the complex network of financial transactions and companies that one would expect to find behind any Russian investments in Mr. Trump’s company or his various real-estate ventures, tax experts said.

“A Russian would not lend directly to Trump or his businesses,” said Steve Rosenthal, a tax lawyer and senior fellow at the Tax Policy Center in Washington. “A Russian would, for example, fund a Cyprus corporation, which would lend to Trump or his businesses, possibly through other intermediary entities.”

—Richard Rubin
contributed to this article.