Trump, seeking re-election in November, said Monday that he was "constitutionally obligated" to nominate someone to replace Ginsburg, who died Friday of cancer at the age of 87.
“We're looking at five incredible jurists... women that are extraordinary in every way. I mean, honestly, it could be anyone of them, and we're going to be announcing it on Friday or Saturday," he said at a rally in Ohio.
On top of his list for the nomination are Amy Coney Barrett of the Chicago-based 7th US Circuit Court of Appeals and Barbara Lagoa of the Atlanta-based 11th U.S. Circuit Court of Appeals.
Trump earlier had a private meeting at the White House with Barrett.
Once he picks a nominee, it is the Senate's job to vote to confirm the Trump pick.
Trump called on the Senate, controlled by his fellow Republicans, to vote on confirmation before the election in which he is seeking a second term.
“I’d much rather have a vote before the election,” he said. “We have plenty of time to do it.”
Senate majority leader Mitch McConnell has vowed to hold a confirmation vote before the election in a move which prompted Democrats to accuse him of hypocrisy.
McConnell said Monday that there was sufficient time to complete the nomination before the election.