AP/Seth Wenig
But at least one prominent Republican figure is starting to worry that Trump could end up on the general-election ballot in another way: by running as a third party candidate.
At a meeting of Republican strategists and lobbyists reported by the New York Times on Thursday, former Republican congressman Thomas Davis raised the possibility that Trump could play spoiler as a third-party candidate.
"You've got to keep him in the tent," Davis told the Times. "He's Ross Perot as an independent. He just wreaks havoc, and every vote he takes comes out of our hide."
According to the Times, members at the dinner said that the party needs to tread carefully as not to alienate Trump, who could be inspired to run as an independent candidate if he is shunned by the Republican Party. The dinner meeting featured "some of the capital's leading Republican elected officials, strategists and lobbyists," according to the Times.
Though in the past he has denied that he wants to run as a third party candidate, Trump's statements this week indicate that he may be warming up to the idea. The Washington Post reported on Thursday that the real estate mogul is leaving the door open to a third party run, depending on who the eventual nominee is.
"So many people want me to run as an independent - so many people," Trump said, according to the Washington Post. "I have been asked by - you have no idea, everybody wants me to do it. I think the best chance of defeating the Democrats and to make America great again is to win as a Republican because I don't want to be splitting up votes."
This is a decided shift from only a few days ago when Trump said that he is not considering running as a third-party candidate. The real-estate mogul told The Washington Examiner that Perot's run was a disaster that helped Bill Clinton win the presidency in 1992.
"It's something I'm not thinking about right now," Trump said, according to the Washington Examiner. "I'm doing well within the Republican ranks, and that gives us the best chance of defeating Hillary Clinton."
There's already plenty of friction between Trump and the Republican Party. Many Republican presidential candidates - including former Florida Gov. Jeb Bush (R), Sen. Marco Rubio (R-Florida), and Sen. Lindsey Graham (R-South Carolina) - have criticized Trumps comments disparaging Mexican immigrants.
On Wednesday, The Washington Post reported that Republican National Committee Chairman Reince Priebus, who attended the dinner meeting with strategists, said that he called Trump requesting that the real-estate mogul tone down his rhetoric.
Trump on Thursday denied that the call was anything but friendly.
Totally false reporting on my call with @Reince Priebus. He called me, ten minutes, said I hit a "nerve", doing well, end!
- Donald J. Trump (@realDonaldTrump) July 9, 2015