President Donald Trump’s search for a Supreme Court justice to succeed Anthony Kennedy is focusing on a trio of federal judges, with a decision expected this week in anticipation of an announcement on Monday, people familiar with the search said.

Following a brisk round of interviews Monday and Tuesday, the three front-runners at this late stage in the president’s search are all U.S. appeals court judges: Brett Kavanaugh of Maryland, of the D.C. Circuit; Raymond Kethledge of Michigan, of the Sixth Circuit; and Amy Coney Barrett of Indiana, of the Seventh Circuit.

Mr. Trump, who spent part of the Fourth of July holiday at his golf club in northern Virginia, has been taking advice from lawmakers and trusted confidants as he settles on a nominee who could set a new direction for a high court split between conservative and liberal factions that have dueled for years.

Since Justice Kennedy was often a swing vote, Mr. Trump’s selection could tip the balance when it comes to some of the most divisive issues the court faces: abortion rights, health care and the limits of executive power, among them.

Advisers in recent days have called Mr. Trump to talk up the merits of different candidates.