Trump is said to want whichever nominee he picks for the high court to be confirmed by mid September, which means there should be a nominee very soon:
BLOOMBERG – President Donald Trump aims to have a replacement for retiring Supreme Court Justice Anthony Kennedy confirmed in time to join the court for its new term in October, White House legislative affairs director Marc Short said.
“Our expectation again would be that we would nominate a candidate in the near future,” Short told reporters Friday at the White House.
The nominee would ideally go through a confirmation hearing and meet with Senate Judiciary Committee members over the summer, with a vote by the full Senate after Labor Day, he said.
Trump will ask potential nominees “about their past, their history, their academic credentials. Questions about things that they’ve written.” But he won’t ask about specific cases or decisions such as Roe v. Wade, the landmark abortion ruling Short said.
Last year, Gorsuch was nominated on Jan 31st and he was confirmed on April 7. That’s roughly a two and a half month turnaround, which is pretty quick. It appears Trump is looking at a similar turnaround on his replacement for Kennedy, assuming someone is nominated in the next couple weeks.