WASHINGTON - Popular Ohio governor John Kasich said in an interview with CNN he is still deeply uneasy with Donald Trump as the Republican presidential nominee, declining to endorse him and reiterating that he will not serve as the tycoon's vice-president.

Kasich, who ended his own presidential campaign earlier this month, has been touted as a potential V-P. As the popular governor of Ohio and a former congressman, Kasich could bring Trump establishment experience and help win a crucial swing state.

But he told CNN his political view was incompatible with Trump's and he was "not inclined" to run with Trump and that he had "not changed my mind".

"Those are two very inconsistent messages, so it would be very hard for me -- unless he were to change all of his views and become a uniter -- for me to get in the middle of this thing," Kasich told CNN's Anderson Cooper in an exclusive interview on Monday (May 16), his first since leaving the race.

"Because, you know, I'm undecided here about what I'm gonna do in this race."

Kasich also warned that Trump is set to lose in the national election on Nov 8 should he persist with his antagonistic political posture that has offended minorities and women.

He also quashed hopes by Republican elites that he might mount a third party bid for the White House. Kasich acknowledged that he had had a phone call with "somebody" who wanted him to mount an independent bid.

"I'm not gonna do that," Kasich said. "I gave it my best where I am. I just think running third party doesn't feel right. I think it's not constructive."