John Kasich doesn't know if he can support Donald Trump for president.

"Hard to say," the GOP governor of Ohio said in an interview on Fox News' "America's Newsroom" Thursday. "Right now, the divisiveness, the division, the name calling -- it just doesn't go down well with me."

Asked if it's possible for him to walk into the Republican National Convention in Cleveland in July and not endorse Trump, Kasich said, "Absolutely. Of course."

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"It's a matter of who I think or what I think we need in order to get this country moving in the right direction. I'm not going to endorse Hillary Clinton, that's for sure," he added.

Kasich said that if Trump, the presumptive GOP presidential nominee, comes into the convention in Ohio and is a "divider," then he won't win his state. He slammed Trump for questioning whether the federal judge overseeing the Trump University lawsuits can be impartial because of his Mexican heritage.

"This latest thing about this judge -- it's terrible, it's just terrible. Look, I think the country needs a leader who can unify. A country needs a leader who can inspire confidence in everyone and make everybody feel like they're special," Kasich said.

Kasich was the last Republican to drop out of the presidential race in early May, just after Ted Cruz suspended his campaign.