The nine-member court has a vacancy, created when Antonin Scalia died on Feb. 13 in Texas.
The list includes two appellate judges, Diane Sykes and William Pryor, who were earlier mentioned by the Republican candidate as good choices. Sykes was married to Charles Sykes, a conservative radio host who led an anti-Trump campaign in Wisconsin, from 1980 to 1999.
Other names on the list are: Steven Colloton of Iowa, Allison Eid of Colorado, Raymond Gruender of Missouri, Thomas Hardiman of Pennsylvania, Raymond Kethledge of Michigan, Joan Larsen of Michigan, Thomas Lee of Utah, David Stras of Minnesota and Don Willett of Texas.
In releasing the names, Trump said the "the list of potential Supreme Court justices is representative of the kind of constitutional principles I value and, as President, I plan to use this list as a guide to nominate our next United States Supreme Court Justices."
Trump told reporters that The Heritage Foundation, a conservative think tank, was helping him compose a list.
Trump has said the next president should be able to name Scalia's replacement.
In his statement, Trump said: "Justice Scalia was a remarkable person and a brilliant Supreme Court Justice. His career was defined by his reverence for the Constitution and his legacy of protecting Americans' most cherished freedoms. He was a Justice who did not believe in legislating from the bench and he is a person whom I held in the highest regard and will always greatly respect his intelligence and conviction to uphold the Constitution of our country."