She would replace the liberal justice, Stephen Breyer, who is expected to retire at the end of the current Supreme Court term in June.
His retirement plans are yet to be officially confirmed.
Justice Breyer’s replacement would not shift the court’s current 6-3 conservative majority.
Each of the nine judges – known as justices – serves a lifetime appointment after being nominated by the president and approved by the Senate.
Ketanji Brown Jackson, 51, a former law clerk to Mr Breyer, is believed to be the top contender for the job.
Ms Jackson was confirmed last June to a seat on the US Circuit Court of Appeals for the District of Columbia, in which she succeeded current Attorney General Merrick Garland.
Leondra Kruger, 45, who serves on the California Supreme Court, is another possibility.
Another tipped contender is J Michelle Childs, a judge on South Carolina’s federal court.
