"It's an improvement to the debate. The IQ of the debate went up a couple dozen points, I would say," he told Fox News Wednesday morning.
"He thinks he's already elected himself king. I say, good riddance. We're going to have a much better debate," Paul added.
Paul is returning to the debate stage after he boycotted the last Republican event earlier this month because Fox Business Network assigned him to the "undercard" stage.
"It's sort of a double win for me. Not only am I on the main stage ... I think we'll have the best debate we've ever had," Paul said.
Speaking to CNN's Jake Tapper on "The Lead" later Wednesday, Paul suggested that Trump should attend the Democratic debate.
"Most of his life he's been a Democrat. Maybe he'll go to the Democratic debate instead. He's somewhat mercurial and unpredictable, so maybe he'll show up at the Democratic debate," Paul said.
Florida Sen. Marco Rubio, meanwhile, said he didn't "have time for these kinds of distractions."
"These kinds of theatrics by Ted Cruz and Donald Trump are an entertaining sideshow, but they have nothing to do with defeating Hillary Clinton," Rubio said in a statement.
"I'm going to stay focused on uniting the Republican party so we can defeat Hillary Clinton and turn the page on eight years of liberal failure. We don't have time for these kinds of distractions."
Trump is openly feuding with Fox News following months of tension between the GOP front-runner and Fox News host Megyn Kelly.
Instead of attending the debate, Trump's campaign manager, Corey Lewandowski, said they will hold an event in Iowa to raise money for wounded veterans.
"And Fox will go from probably having 24 million viewers to about 2 million," he said.