The US Department of Justice says it has asked prosecutors to scrutinise the Clintons' charitable foundation and a uranium deal.
Attorney General Jeff Sessions said a top-level inquiry could be launched into "certain issues" at the Clinton Foundation and the sale of Uranium One.
Jeff Sessions outlined the move in response to a letter from congressional Republicans.
The matters are longstanding political grievances of President Donald Trump.
Democrats have called Uranium One a "massive diversion" from the investigations dogging Trump's presidency.
His aides are currently the focus of inquiries by a special counsel and congressional committees into whether they colluded with alleged Kremlin attempts to sway last year's US presidential election.
What is Uranium One?
Uranium One - a Canadian mining company that owned a fifth of US uranium supplies - was acquired in 2010 by Russian state-owned company Rosatom.
The US Department of State, under former Secretary of State Hillary Clinton, helped approve the 2010 deal, along with former President Barack Obama.
Republicans have charged that the Department of State approved the deal after Bill Clinton's charitable foundation received a $145m (£110m) donation.
Some of those contributions were not publicly disclosed by the Clintons, despite their pledge to publicly identify all donors, the New York Times reports.
Bill Clinton was also paid $500,000 for a Moscow speech from a Kremlin-linked Russian investment bank that was promoting shares in Uranium One.
What is the Justice Department doing?
The chairman of the House of Representatives Judiciary Committee, Robert Goodlatte, wrote to the Department of Justice recommending that a special counsel look into the Uranium One deal.
US media report that a reply from the US attorney general's deputy said he had "directed senior federal prosecutors to evaluate certain issues raised in your letters".
The Department of Justice cited "alleged unlawful dealings related to the Clinton Foundation and other matters".
The agency also said it would decide "whether any matters merit the appointment of a Special Counsel".
Republican lawmakers announced last month they were investigating the Uranium One sale.
They launched another inquiry relating to Hillary Clinton's misuse of a personal email server.
Is the Justice Department independent?
The president wields significant constitutional authority over the Department of Justice since it belongs to the executive branch of US government.
But it has been a US civic tenet ever since the Watergate scandal that the agency should be free from political interference.
Trump acknowledged this in a radio interview this month, when he said "the saddest thing" was that he was not supposed to meddle with the Justice Department.
However, the Republican president has also publicly called on his attorney general to open an investigation into Hillary Clinton.
He tweeted that America's top prosecutor had "taken a VERY weak position on Hillary Clinton crimes".
"So where is the investigation AG?" Trump asked.