President Joe Biden met with Senate Majority Leader Chuck Schumer at the White House on Wednesday to talk about how to fill an upcoming vacancy on the Supreme Court, according to a person familiar with the negotiations.

President Biden has promised to nominate the first Black woman to the high court to fill the spot being vacated by Justice Stephen G. Breyer, who is retiring at the end of this term. The president, who has promised to make a decision by the end of the month, has amassed a list of potential candidates that includes women with a range of professional expertise, from federal defenders to longtime judges and academics.

Sen. Schumer, D-N.Y., has promised the Senate will have a fair process that moves quickly to fill the vacancy. His meeting with President Biden was confirmed by a person who was not authorized to speak publicly about private events and spoke to AP on condition of anonymity. On Tuesday, President Biden played host to Judiciary Committee Chairman Dick Durbin, D-Ill., and ranking Republican Chuck Grassley, R-Iowa. The president also spoke by phone with Senate Minority Leader Mitch McConnell, R-Ky.

The court was made up entirely of white men for almost two centuries. Justice Clarence Thomas and the late Thurgood Marshall are the only two Black men who have served on the court. There has never been a Black woman.

Among the candidates under consideration are Ketanji Brown Jackson, who serves on the U.S. Court of Appeals for the District of Columbia Circuit, U.S. District Court Judge J. Michelle Childs from South Carolina, California Supreme Court Justice Leondra Kruger, U.S. District Court Judge Wilhelmina Wright from Minnesota and Melissa Murray, a New York University law professor who is an expert in family law and reproductive rights justice.

According to people familiar with the discussions, another name in the mix is Leslie Abrams Gardner, a U.S. district judge for the Middle District of Georgia and the sister of Stacey Abrams, a powerful voting rights activist and nominee for Georgia governor.

President Biden, who led the Judiciary Committee through six nominations during his time as a Delaware senator, said Tuesday that he planned to seek the “advice and consent” of senators during the process, and he is hoping for a bipartisan nominee.

Two Republicans signaled they could vote for President Biden’s nominee — if it is the right one. South Carolina Sens. Lindsey Graham and Tim Scott have both praised Ms. Childs, who got her law degree from the University of South Carolina School of Law. She is also the favorite of Majority Whip Jim Clyburn, a powerful Democratic ally.

Sen. Graham on Wednesday tweeted out a photo of the three South Carolina lawmakers sitting together at lunch. “Great fellowship today with my colleagues” he wrote. Sen. Graham also said his vote would be “much more problematic” if Judge Childs is not the nominee.

Former Alabama Sen. Doug Jones, a Democrat who often crossed party lines before he was defeated for reelection in 2020, will serve as the lead official for the White House to shepherd the nomination.