"Trump is an actor playing the role of a presidential candidate," Bush said, upping the ante against the billionaire.
The duo is engaged in a heated debate about the 9/11 attacks after Trump slammed Bush's elder brother and former US president George W Bush on the weekend, holding him partially responsible for the attacks which happened in 2001 during his presidency.
"I have grave doubts, to be honest with you," Bush told CNN in an interview.
"Across the spectrum of foreign policy, Trump talks about things as though he's still on 'The Apprentice'," Bush said, making a reference to the popular US reality game show hosted by Trump.
"It gives me great concern," said the former Florida Governor, who is trailing behind Trump in all national polls.
Accepting that "Trump is a phenomenal personality," Bush, however, predicted that he will not succeed in winning the Republican party nomination.
He also offered a rare praise for Democratic front-runner Hillary Clinton's debate performance.
"She did a good job in the debate, for sure. She's a smart person, no doubt about that. But every chance she had to lay out a different approach than the one we're on now, she actually doubled or tripled down on it, more taxes, more regulation, more creating barriers on people's ability to rise up," Bush said.
