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Trump lacks right temperament for presidency: Zell

Real estate mogul Sam Zell said Wednesday that fellow property billionaire and GOP presidential front-runner Donald Trump does not have the right personality for the White House.

"I know Don. I think Don is a very accomplished person," Zell told CNBC's "Squawk Box," adding it would be a "big mistake" to underestimate Trump.

"But on the other hand," Zell argued, "I doubt that [Trump] has the temperament and the personality to be the president of the United States."

Zell said he has a "great deal of trouble believing" why Trump would even want to be president, because the office comes with a "very different definition of power."

Read More Sam Zell: Wall Street, Main Street out of sync

Trump, who's positioned himself as a Washington outsider willing to tear up the political playbook, is known for bold and sometimes controversial statements.

"You can't be president of the United States and throw out all the rules, because everybody else has an interest," said Zell, who questioned how much longer the nonpoliticians can top the still-crowded Republican field.

But Zell said it's clear the "American people are really pissed off," and they're responding to anything that's different.

In the latest RealClear Politics polling aggregator, retired neurosurgeon Ben Carson and former Hewlett-Packard CEO Carly Fiorina occupied second and third place, respectively.

While Trump remains No. 1, his lead has shrunk since a month ago in the early Republican nominating contests states of Iowa and New Hampshire, according to recent polls conducted by NBC News/Wall Street Journal/Marist.

The surveys in those two states, conducted Sept. 23-30, were after the second GOP debate on CNN and after Wisconsin Gov. Scott Walker withdrew from the race. CNBC hosts the next Republican debate in Boulder, Colorado, on Oct. 28.

Reluctant to name names, Zell said it would be impossible for him to support five or six of the GOP candidates because, while fiscally conservative, he's socially liberal. He did put Carson in that camp, but said he didn't know enough about Fiorina to make a judgment on her candidacy.

Read MoreBen Carson: 6-month tax hiatus for overseas profits

Zell also said he has ruled out Chris Christie, not on the basis of social issues, but because "he's damaged goods," arguing that the New Jersey governor missed his window to run for president in 2012 when he said he wasn't ready.

Zell did say he could support Ohio Gov. John Kasich, Florida Sen. Marco Rubio or ex-Florida Gov. Jeb Bush, all of whom have been struggling in the polls.

But it's a long road until Election Day, Zell noted, arguing that a presidential race can change dramatically.

"Four years ago at this time, [businessman] Herman Cain was leading in the polls," Zell recalled. The former Godfather's Pizza CEO dropped out of the race in 2011 shortly before the Iowa Caucus.

Mitt Romney, a former governor of Massachusetts, was the eventual GOP nominee in 2012. But he lost in his bid to deny President Barack Obama a second term.

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