It was not clear whom the president had chosen to nominate to succeed Justice Stephen Breyer, who is retiring this year.
Names that have been mentioned as finalists include those of Ketanji Brown Jackson and J. Michelle Childs, who are both federal judges, and California Supreme Court Justice Leondra Kruger. Sources familiar with the matter confirmed this week that Biden had spoken with the three judges.
A source said Thursday that an announcement could come before the weekend.
CNN first reported that Biden had reached a decision.
The White House has said Biden, who as a presidential candidate pledged to nominate a Black woman to the court for the first time in U.S. history, will make his decision known by Monday.
More from NBC News
Earlier Thursday, White House press secretary Jen Psaki said the administration was on track to make an announcement by Monday, but when she was asked whether a final decision had been made, she said: "Not a 'final final.'"
"No job offer has been made," she added.
NBC News reported Thursday that Biden had a meeting in the Oval Office on Wednesday with Dana Remus, the White House counsel, and his director of legislative affairs, Louisa Terrell, on consultations with senators about the Supreme Court.
Breyer, 83, announced last month that he would step down at the end of the current Supreme Court term. With 27 years on the bench, he is the second-longest-serving justice after Clarence Thomas.