The White House is focusing on five to seven potential candidates to fill the vacancy of retiring Justice Anthony Kennedy, who was a swing vote on the court. The nominees reportedly include two women.
Trump now has the chance to create a conservative majority on the court for years to come.
In a Fox News interview, the president was asked if his nominee will be confirmed before the fall midterm elections.
"I think it's going to go very quickly," he replied. "I think we're going to have a lot of support. I think we're going to have a lot of support from Democrats, frankly. If it's the right person, I'm going to pick the right person. I'm going to pick somebody who is outstanding. And everybody on that list is outstanding. And I think, yes, I think it will go very quickly. "
Who would African American Evangelicals like to see President Trump choose to replace Justice Kennedy at the U.S. Supreme Court? Glory to Glory Ministries Pastor Aubrey Shines discusses why the president should choose a pro-life justice and why a growing number of blacks are standing up against abortion.
Meanwhile, Democrats are already on the attack, fearing Trump's pick will help the court overturn the 1973 Roe v. Wade decision that legalized abortion.
Standing outside the Supreme Court, New York Democratic Sen. Kirsten Gillibrand told supporters, "Women's lives are at stake. Make no mistake. This is about whether we are going to criminalize women's health care decisions."
It's not just Democrats that Trump has to worry about. Some key pro-choice Republicans could also give him trouble.
Sen. Susan Collins (R-Maine) said Sunday she would oppose any nominee she believed would overturn Roe v. Wade.
"A candidate of this important position who would overturn Roe v. Wade would not be acceptable to me because that would indicate an activist agenda," Collins told ABC's "This Week."
When asked if he will he ask his nominee about Roe V. Wade, Trump replied, "They're all saying, 'Don't do that. You don't do that. You shouldn't do that.' But I'm putting conservative people on."
"I'm very proud of Neil Gorsuch," he continued. "He has been outstanding; his opinions are so well-written, so brilliant. I'm going to try to do something like that, but I don't think I'm going to be so specific in the questions I'll be answering and I'm actually told that I shouldn't be."
Meanwhile, evangelical leaders, like Jerry Falwell Jr., are downplaying a potential reversal of Roe v. Wade. He points out the issue would simply be returned to the states and that a majority of states would keep abortion legal.