He told Fox & Friends on Monday that he had a list of five finalists, “probably four”, and that he is pushing for a confirmation vote before election day.
Mr Trump disparaged reports that Ms Ginsburg had told her granddaughter it was her wish that a replacement justice not be confirmed until the inauguration of a new president.
Mr Trump said he thought his Democratic political foes were behind the report, including Representative Adam Schiff, who led the House impeachment probe, House Speaker Nancy Pelosi, and Senate Democratic Leader Chuck Schumer.
“I don’t know that she said that, or was that written out by Adam Schiff and Schumer and Pelosi,” Mr Trump said.
“I would be more inclined to the second … But that sounds like a Schumer deal or maybe a Pelosi or Shifty Schiff,” using his nickname for the California congressman.