Speaker of the House Rep. Nancy Pelosi (D-CA) speaks during a weekly news conference at the U.S. Capitol February 14, 2019 in Washington, DC.

The Trump administration is in early talks with House Speaker Nancy Pelosi about possible legislation to lower prescription drug costs, a White House official confirmed.

"Lowering the cost of prescription drugs is a shared common interest, and those conversations will continue," the person said, asking not to be identified because the discussions aren't public.

The official wouldn't say what the legislation might look like or when a bill might be introduced. Politico first reported the news.

High drug costs have become a rare bipartisan issue, with lawmakers on both sides of the aisle demanding something be done. President Donald Trump has made lowering prices one of his key issues ahead of the 2020 election. Democrats are also jockeying to prove they can lead reform.

Last month, top executives from AbbVie, AstraZeneca, Bristol-Myers Squibb, Johnson & Johnson, Merck, Pfizer and Sanofi testified before the Senate Finance Committee about high prescription drug costs. Spending on prescription drugs in the U.S. increased to $333.4 billion in 2017, according to data from the Centers for Medicare and Medicaid Services.

Drug companies argue that price increases have been modest, and have instead pointed the blame at pharmacy benefit managers, sometimes called middlemen. They say that PBMs should pass the rebates negotiated with manufacturers along to patients. Drugmakers applauded the administration's pursuit to change the nation's rebate system.

White House Domestic Policy Council Director Joe Grogan and legislative director Shahira Knight are leading the talks for the Trump administration. Wendell Primus, Pelosi's health policy staffer, is leading the talks for the House Democrats.

"We've been having some staff-level discussions with the administration about lowering prescription drug prices, but they aren't negotiations," Pelosi spokesman Henry Connelly told CNBC.

"House Democrats promised the American people we'd take bold action to lower prescription drug prices, and that's what we're going to do," he added.

--CNBC's Ylan Mui contributed to this report.