In May, after the death of Justice Antonin Scalia, an anchor of the court's conservative majority, Trump listed 11 names he said he would consider nominating if he were elected president. The list was an effort to quell conservatives anxious he would not choose someone in Scalia's mold, threatening their majority on the bench.
On Friday, with President Barack Obama's nomination of Merrick Garland floundering in the Senate, Trump added 10 more names to his list -- five federal appellate judges, four state Supreme Court judges and Lee, Utah's junior senator and a former federal prosecutor who previously clerked under Justice Samuel Alito.
Lee, one of the Senate's most conservative members, said through a spokesman he would not want to leave his post in the Senate. Lee has also thus far declined to endorse Trump after backing Texas Sen. Ted Cruz in the Republican primary.
"Sen. Lee already has the job he wants, which is why he is campaigning to represent the great people of Utah again this year," Lee spokesman Conn Carroll told Politico.
Trump said the full list of 21 names is "definitive" and no one else would be considered.
Lee's brother, Thomas Lee, a state Supreme Court judge in Utah, was included on Trump's initial list of potential nominees.
Trump's full list includes:
-- Keith Blackwell, Georgia Supreme Court -- Charles Canady, Florida Supreme Court -- Steven Colloton, 8th Circuit Court of Appeals -- Allison Eid, Colorado Supreme Court -- Neil Gorsuch, 10th Circuit Court of Appeals -- Raymond Gruender, 8th Circuit Court of Appeals -- Thomas Hardiman, 3rd Circuit Court of Appeals -- Raymond Kethledge, 6th Circuit Court of Appeals -- Joan Larsen, Michigan Supreme Court -- Sen. Mike Lee, R-Utah -- Thomas Lee, Utah Supreme Court -- Edward Mansfield, Iowa Supreme Court -- Federico Moreno, U.S. District Court for the Southern District of Florida -- William Pryor, 11th Circuit Court of Appeals -- Margaret A. Ryan, U.S. Court of Appeals for the Armed Forces -- David Stras, Minnesota Supreme Court -- Diane Sykes, 7th Circuit Court of Appeals -- Amul Thapar, U.S. District Court for the Eastern District of Kentucky -- Timothy Tymkovich, 10th Circuit Court of Appeals -- Don Willett, Texas Supreme Court -- Robert Young, Chief Justice, Michigan Supreme Court