President Trump has said he will name a replacement to Ruth Bader Ginsburg before the end of this week, and urged the Republican controlled Senate to confirm his choice before 3rd November.
The plan has launched a high-stakes battle ahead of the election.
Mr Trump would replace Ginsburg, a liberal stalwart who died on Friday aged 87, with a conservative.
The president appears to have secured enough support in the US Senate to win approval for his nominee.
This would cement a right-leaning majority on the court for decades.