The Senate Intelligence Committee asked for the records from the Treasury's Financial Crimes Enforcement Network, or FinCEN, late last month, the Journal cited the people as saying.
One person said the records were needed to decide whether there was collusion between Trump associates and Russia during the 2016 campaign, the Journal said.
Representatives for FinCEN and Republican Senator Richard Burr, the intelligence committee chairman, declined to comment, the Journal said.
According to Reuters, the Senate probe took on added significance after Trump dismissed FBI Director James Comey earlier this week amid an agency investigation into alleged Russian meddling in the 2016 U.S. presidential election and possible Moscow ties to the Trump presidential campaign. The House of Representatives intelligence panel is conducting a similar probe.