President Donald Trump said Tuesday that while he believes his daughter, Ivanka Trump, would make an "incredible" U.S. ambassador to the U.N., he would be accused of "nepotism" if he named her.

"How good would Ivanka be?" he asked rhetorically before dismissing the idea.

"I think Ivanka would be incredible but it doesn't mean [I would name her]," Trump said. "I would be accused of nepotism." He added that he thought there was no one "more competent in the world" than Ivanka Trump.

White House adviser Ivanka Trump listens during a meeting between U.S. President Donald Trump and Nikki Haley, the United States Ambassador to the United Nations in the Oval office of the White House Octo. 9, 2018 in Washington, DC. Olivier Douliery / AFP - Getty Images

Speaking to reporters on the South Lawn of the White House just hours after Nikki Haley announced that she would be leaving the prestigious diplomatic post, Trump said that Ivanka Trump, who currently serves as a White House adviser to him, would be competent for the job but that he would face nepotism charges if he appointed her to it.

Shortly after her father's remarks, Ivanka Trump said on Twitter that she had no interest in succeeding Haley.

"That replacement will not be me," she said.

It is an honor to serve in the White House alongside so many great colleagues and I know that the President will nominate a formidable replacement for Ambassador Haley. That replacement will not be me. — Ivanka Trump (@IvankaTrump) October 9, 2018

Federal law may preclude the president from appointing relatives to the U.N. ambassadorship, since it would be considered a post within an executive agency.

Trump will have some time to replace Haley, who appeared with him at the White House earlier Tuesday, because her resignation won't be effective until the end of the year.

Trump confirmed that Dina Powell, a former deputy national security adviser in his administration, could get the U.N. job.

"Dina is a person I would consider," he said, adding that there are "many names" that might be in the mix.

Later, as he traveled to Iowa for a reelection campaign rally on Air Force One, Trump told reporters that he had a short list of five candidates for Haley's job that includes Powell but not U.S. Ambassador to Germany Richard Grenell.

"He is doing so well in a position that is so important," Trump said. "I wouldn't want to move him. I'd personally rather keep Ric where he is."

Of Powell, Trump said, "Dina would love it."