Republicans are laying the groundwork for a swift confirmation process for Ms Barrett, even before Mr Trump makes the selection official in a Rose Garden ceremony on Saturday evening.
For days, White House officials have indicated to allies that Ms Barrett is Mr Trump’s pick, but aides have offered no official word as they try to maintain some suspense before the official announcement.
Mr Trump said: “We’re going to be naming the nominee who hopefully will be on that court for 50 years. The only thing I can tell you for sure is it will be a woman.”
It comes after former Supreme Court justice Ruth Bader Ginsburg, a liberal, died earlier this month.
The likely shift in the court’s make-up — from liberal icon Ms Ginsburg to Ms Barrett, an outspoken conservative — would be the sharpest ideological swing since Clarence Thomas replaced Justice Thurgood Marshall nearly three decades ago.
Senate Republicans are readying for confirmation hearings in two weeks, with a vote in the full chamber now expected before Election Day on November 3. Democrats are powerless to block the votes.
“I’m confident he’s going to make an outstanding nomination,” Senate Majority Leader Mitch McConnell told Fox News.
“The American people are going to take a look at this nominee and conclude, as we are likely to conclude, that she well deserves to be confirmed to the US Supreme Court.”
“They’re hell-bent on getting this done as fast as possible,” said Democratic Senate whip Dick Durbin. “They think it helps Donald Trump get re-elected.”
Within hours of Ms Ginsburg’s death, Mr Trump made clear his intention to nominate a woman in her place, after previously putting two men on the court and as he struggles to mitigate an erosion in support among suburban women.
The White House has already concluded a round of vetting this month, as Mr Trump released an additional 20 names he would consider for the court. He has challenged Democrat Joe Biden to list possible nominees too.
Mr Trump had said he was considering five women for Ginsburg’s seat, including Florida’s Barbara Lagoa and Michigan’s Joan Larsen.
Ms Barrett, of Indiana, was at the White House at least twice this week, including for a Monday meeting with Mr Trump. He is not known to have met with any of the other contenders.
With additional reporting by the Associated Press