Barret will replace liberal Justice Ruth Bader Ginsburg, who died last Friday. The decision is likely to be announced at the White House on Saturday, the international media reported.
The nomination will touch off a bitter Senate fight to get her confirmed as November’s White House election looms.
CBS – citing multiple sources involved in or familiar with the selection process – reported that the president had settled on Judge Barrett.
If she is confirmed, conservative-leaning justices will hold a 6-3 majority on America’s highest court for the foreseeable future.
Amy Coney Barrett, 48, would be the third justice appointed by this Republican president to the bench, after Neil Gorsuch in 2017 and Brett Kavanaugh in 2018.
Its nine justices serve lifetime appointments, and their rulings can shape public policy on everything from gun and voting rights to abortion and campaign finance long after the presidents who appoint them leave office.
In recent years, the court has expanded gay marriage to all 50 states, allowed for Trump’s travel ban to be put in place, and delayed a US plan to cut carbon emissions while appeals went forward.