Last Friday, the liberal judge Ruth Bader Ginsburg, 87 years old, died.
Now President Trump will nominate his candidate to replace him.
According to several American media, he will nominate conservative Amy Coney Barrett.
CNN was the first to publish the news, citing several Republican sources with insight into the process.
According to sources, she is the only potential candidate the president has met in person.
The New York Times and the Wall Street Journal also have the same information, as does the news agency Reuters, which, however, writes that Trump may change at the last minute.
Described her as "outstanding"
When the president received the question from journalists on Saturday night, Swedish time, the answer was that he decided "in his own head".
However, he did not want to confirm whether it was 48-year-old Amy Coney Barrett, but said that Coney Barrett is "outstanding".
Amy Coney Barrett is a former law professor, who is a respected name in conservative circles and the mother of seven is known for her fierce abortion resistance.
Barrett is also a devout Catholic and popular with the religious right.
Since 2017, she has been a federal judge on the Court of Appeals for the Seventh District of the United States (which includes Illinois, Indiana and Wisconsin).
If Trump chooses to nominate a Conservative judge, it means that a total of nine judges in the US Supreme Court can gain a Conservative overweight of 6-3.