Trump told reporters on board the presidential aircraft Air Force One he had narrowed the choice down to “about five” candidates, including two women.
The vacancy arose when Justice Anthony Kennedy announced his retirement earlier this week.
It gives President Trump the opportunity to solidify a conservative majority on the top court.
His nominee will need to be confirmed by the Senate where the president’s Republican Party holds a narrow majority.
In other comments to reporters on Friday, Mr Trump:
Said he would discuss allegations of election tampering when he met Russian President Vladimir Putin in Helsinki next month
Called on Germany and other European nations to spend more on Nato, adding: “The United States is paying much more, disproportionately to anyone else”
Said the World Trade Organization (WTO) had treated the US “very badly” but insisted he was “not talking about pulling out”
Source – BBC