Washington (CNN) Nikki Haley's surprise resignation as the US ambassador to the United Nations raises the next question: Who fills her shoes?

As President Donald Trump heaped praise on Haley's performance during her tenure as the American representative to the world body, he said many people would like to replace her.

"We have a number of people who would very much like to do it," Trump said, speaking in the Oval Office with Haley at his side. "It's a great position ... she's helped make it a much better position."

Trump told reporters that he expects to name a replacement for Haley in the next "two to three weeks," and said that he would be talking about candidates with the former South Carolina governor and others. Haley will serve until the end of the year , he said.

"I can say many people want to do it and they want to do it," Trump said.

Who's next?

Names that are already being bandied about include Dina Powell, a close confidante of first daughter Ivanka Trump who served as Trump's deputy national security adviser for Strategy. Powell, who came to the White House from Goldman Sachs, was a favorite of Trump's before her resignation after a year.

Powell, who returned to Goldman Sachs and is also a senior fellow at Harvard University, was deeply involved in the administration's Middle East policy and was instrumental in planning all of Trump's overseas trips as well as his debut at the United Nations General Assembly in September 2017.

Another name being discussed is the current ambassador to Germany, Rick Grenell.

A Michigan native who ruffled feathers in Germany with his criticism of Berlin's defense spending and comments about "empowering" right-wing parties in Europe, Grenell had previously been the longest-serving US spokesman at the UN.

I am thankful to have a President who is clear in his instructions and always focused on the American people. @realDonaldTrump pic.twitter.com/mbPrO7vhIf — Richard Grenell (@RichardGrenell) October 3, 2018

Part of his tenure was spent working with Trump's national security adviser John Bolton, who served as President George W. Bush's ambassador to the UN. And in his time as Trump's representative to Germany, Grenell has established himself as a fierce and vocal defender of the President and his policies.

"I am thankful to have a President who is clear in his instructions and always focused on the American people," Grenell tweeted on October 3, adding a photo of himself in the Oval Office with a grinning Trump.

Grenell's experience in Germany and at the UN is a great advantage, as are the relationships he built during that time, said Alice Stewart, a Republican strategist and CNN political commentator.

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"I think Rick Grenell would be a tremendous choice," Stewart said. "His experience with international affairs and his relationship with Bolton has set him up in a good spot."

Trump told reporters later Tuesday on Air Force One en route to Iowa that he has five people on his shortlist to replace Haley, but Grenell is not among them.

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

Another name that is floating to the top is much closer to the President -- Ivanka Trump. Though the first daughter would be a very tough sell to get through Senate confirmation hearings, Ivanka has been quietly building close relationships with a lot of lawmakers, working on issues like global economic empowerment for women.

Stewart, reflecting much early opinion, said "I think it sends the wrong message, but it would certainly not surprise me were [Trump] to do so."

CNN contributor and University of Texas law school professor Steve Vladeck says she could not be paid if she took the job, according to a federal anti-nepotism law which technically suggests she couldn't even be appointed but says the penalty for a violation is simply no pay.

A source familiar with discussions says Ivanka Trump laughed Tuesday morning when she heard about the speculation that she could replace Haley.

However, Trump later told reporters that his daughter would be "incredible" as US Ambassador to the United Nations, but said he would be "accused of nepotism" if he appointed her to succeed Haley.

"I've heard a lot of names. I've heard Ivanka. How good would Ivanka be?" Trump said. "I think Ivanka would be incredible but it doesn't mean I'd pick her. Because I'd be accused of nepotism even though I'm not sure there's anybody more competent in the world."

He then said his daughter would be "dynamite" as UN ambassador.

Soon after the President's remarks, Ivanka Trump took to Twitter to rule herself out of the running:

"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."

President Trump, speaking with Haley, noted that being UN ambassador has "become maybe a more glamorous position than it was a few years ago." He added of Haley, "she's made it a more glamorous."