The vacancy on the bench creates what many conservatives view as a once-in-a-generation opportunity to move the makeup of the court from its current split of five conservative justices and four liberal justices to a more dominant 6-3 majority.

CNN previously reported that the President had been "salivating" to nominate a replacement for the liberal justice even before Ginsburg's death Friday and the possibility of picking her successor has weighed on his mind, according to a source close to the President.

The source told CNN that Trump specifically has said he would "love to pick" federal appeals judge Amy Coney Barrett, who is a favorite among religious conservatives, but doubts he'll secure support from the US Senate.

Barrett is among Trump's list of 20 potential conservative nominees he released earlier this month in an attempt to galvanize his base.

A senior administration official told CNN that the White House is prepared to move "very quickly" on putting forward a nominee to replace Ginsburg once Trump signals his intentions.

Ultimately, it will be McConnell's decision and not one he'll make without input from his members in the coming days.

In speaking with reporters Saturday morning, White House press secretary Kayleigh McEnany was asked by CNN's Joe Johns if the President has been in contact with McConnell or other Senate Republicans on next steps.

"Not that I'm aware of," she replied, adding, "Right now the President is squarely focused on honouring the legacy of Justice Ruth Bader Ginsburg."

She called on Democratic presidential nominee Joe Biden to release a list of potential Supreme Court nominees so voters know where he stands.

Before news of Ginsburg's passing, Biden told reporters Friday that he doesn't think he will release any names of potential Supreme Court nominees before the election.

Trump has tried pressuring his 2020 rival to release a similar list, saying that Biden has "refused" to do so "perhaps because he knows the names are so extremely far left that they could never withstand public scrutiny or receive acceptance."

This story has been updated with additional developments Saturday.