Gorbachev calls Trump's withdrawal from arms treaty 'a mistake'
Trump: Five people on short list to replace Haley as UN ambassador
Trump told reporters in his office aboard the presidential aircraft that Dina Powell, his former deputy national security adviser, is on the short list.
"Dina would love it," he said.
Powell left the Trump administration at the beginning of the year after serving as a deputy national security adviser, where she focused on Middle East policy.
Trump said Richard Grenell, the U.S. ambassador to Germany, is not on the short list but he is willing to consider him for the post. Grenell is well-liked among Trump allies and White House staffers.
"He is doing so well in a position that is so important," Trump said. "Rick is doing so well that I wouldn't want to move him. I'd personally rather keep Rick where he is."
Grenell was sworn-in to his role in May following a tense confirmation process during which Trump accused Democrats of blocking Grenell's nomination.
As he departed for Iowa, Trump told reporters at the White House that his daughter, Ivanka Trump, would make an "incredible" ambassador to the United Nations, but conceded that appointing her would lead to accusations of nepotism.
"I think Ivanka would be incredible," he continued. "You'd be accused of nepotism, even though I'm not sure there's anybody more competent in the world."
Ivanka Trump, who also serves as a senior adviser to the president, tweeted a short time later that she would not be replacing Haley.
The president and Haley announced earlier Tuesday that she would depart her post by the end of 2018. The two portrayed Haley's departure as amicable, explaining that she wanted to "take a break" from public service.
Trump said Haley would assist in the search for her replacement, and that he plans to settle on a pick in the next two to three weeks.
"I think she's also brought a new level of prestige to that position," Trump said of Haley. "That position is - in terms of people wanting it - easier now in a way than it was before."
Updated at 6:42 p.m.