The talks on a bilateral deal are a first step toward forming what officials have described as a buyers club for materials central to the clean-energy transition. The trade deal and broader buyers club are aimed at addressing a dispute over U.S. subsidies for electric vehicles, as well as moving clean-energy supply chains away from China.

The Inflation Reduction Act, passed last year, revamped U.S. tax credits for electric vehicles. It required that EV batteries largely contain minerals from the U.S. or a country with which the U.S. has a free-trade agreement. That angered close U.S. allies who don’t have a free-trade agreement with the U.S., including the EU and Japan.

The U.S. is now beginning to craft a deal with the EU that would narrowly focus on environmental and labor standards for producing critical minerals, such as lithium and nickel, according to the people familiar with it. In the U.S., it would be an executive agreement that doesn’t require Congressional approval, according to the people.

While such a deal wouldn’t be a traditional free-trade agreement that lowers tariffs, the Biden administration thinks such a deal would allow the EU to meet the minerals-sourcing requirement for the subsidies, according to the people.

“There could be a designation that the EU, at least in the sector of critical minerals, could be considered a free trade partner,” said Erik Brattberg, a senior fellow at the Atlantic Council.

With an agreement focused on critical minerals, which the U.S. is also pursuing with Japan and the U.K., the Biden administration is trying to appease allies abroad while also not rankling the lawmakers on Capitol Hill who crafted the new rules for the subsidies. Striking that balance might prove difficult.

Sen. Joe Manchin (D., W.Va.), a centrist at the center of crafting the law, has loudly criticized the Biden administration’s previous decisions on how to implement the law, arguing they run afoul of his intent to bring manufacturing to the U.S. Mr. Manchin said Wednesday he would vote against Mr. Biden’s nominee to lead the Internal Revenue Service because of his disapproval of the Treasury Department’s previous efforts to give allies eligibility for elements of the subsidies.

Some lawmakers are also concerned that the Biden administration could create trade policy without their approval. Sen.

Ron Wyden

(D., Ore.)—the chairman of the Senate Finance Committee, which oversees trade policy—has called on the Biden administration to work with lawmakers on its trade moves.

“We’ve made it clear that there is a constitutional imperative that the Congress and the Senate be involved in trade policy,” he said.

The Biden administration is consulting with Congress, as well as labor unions, on the talks, U.S. officials said.

Under the Biden administration’s design, agreements with the EU, Japan and the U.K. would be the first step toward creating a new buyer’s club for critical minerals among the Group of Seven advanced democracies.

The G-7 group would then approach countries in Africa, Asia or Latin America that are rich in minerals and seek agreements with them. U.S. and European officials have started that outreach, according to people familiar with it.

As part of those arrangements, the G-7 would offer to provide financing for developing the infrastructure for procuring the minerals, according to the people familiar with the plans. China is currently a major supplier of minerals for critical clean-energy technologies, drawing concern from Western officials.

The goal of the buyer’s club is to ensure that the Western world has reliable access to critical minerals, while preventing a bidding war between the G-7 economies over them. The Inflation Reduction Act will eventually bar vehicles with any minerals sourced from countries of concern like China from receiving the subsidy.

Write to Andrew Duehren at andrew.duehren@wsj.com