Donald Trump is expected to nominate Amy Coney Barrett to the Supreme Court.
Barrett,48,is a devout Catholic who has long been viewed as a rising star in conservative legal circles. Her appointment would cement a 6-3 conservative majority on the nation's most powerful court.
Ginsburg on Saturday (AEST) became the first woman and the first Jewish American to lie in state at the US Capitol Building in Washington.
Republicans have moved speedily to fill Ginsburg's seat and appear increasingly likely to install her successor before election day on November 3. The Senate Judiciary will hold confirmation hearings before a full vote on the Senate floor.
Trump has directly tied the confirmation of the new justice to the presidential election.
"I think this will end up in the Supreme Court,"Trump said of potential disputes about mail-in-ballots."And I think it’s very important that we have nine justices."
Barrett is viewed by conservatives as particularly appealing because of her relatively young age,which could allow her to serve on the court and make influential rulings for decades to come.