Graham said the candidates discussed included retired Lt. Gen. Keith Kellogg, former acting national security adviser and currently Vice President Pence’s national security adviser; Brian Hook, the State Department’s special envoy for Iran; and Rick Waddell, who served as deputy national security adviser under former national security adviser H.R. McMaster.
Graham added there were “others” floated, too, without naming them.
“I think he’ll make a good choice here next week,” Graham told reporters.
Trump told reporters in the Oval Office on Wednesday afternoon he has five candidates to replace Bolton, reiterating he would make an announcement on his pick next week.
Trump tweeted Tuesday he had fired Bolton by telling him Monday evening “that his services are no longer needed at the White House,” pointing to disagreements with the national security adviser and others in the administration.
But Bolton disputed his account, tweeting that he offered to resign on Monday and that Trump had asked to talk about it the following day.
Bolton’s departure ended an 18-month tenure as Trump’s top security adviser in which he saw his influence steadily wane.
The pair clashed on a number of foreign policy fronts, including Trump’s efforts to negotiate a peace agreement with Afghanistan and the president’s increasing openness to talks with Iran.
On Wednesday, Trump specifically cited Bolton’s early misstep in floating a “Libya model” for nuclear negotiations with North Korea.
Bolton had suggested the United States approach nuclear negotiations with North Korea as it did with Libya. The comments nearly scuttled then-nascent diplomacy with North Korea, who feared Bolton meant its leaders would meet the same fate as killed Libyan strongman Moammar Gadhafi.