Presumptive Republican nominee Donald TrumpDonald John TrumpAccuser says Trump should be afraid of the truth Woman behind pro-Trump Facebook page denies being influenced by Russians Shulkin says he has White House approval to root out 'subversion' at VA MORE says there's a decent chance he picks a former rival in the presidential race to be his running mate.

Trump on Thursday told CNBC's "Squawk Box" there's "probably a 40 percent chance" he'll pick someone who ran in the GOP primary.

"I've gotten to be friends with a lot of those people, and I guess, perhaps, enemies with a couple," he said. "I would say there's a good 40 percent chance."

Trump has begun the vetting process for his vice presidential pick, spurring what will likely be months of rumors and speculation about his eventual choice.

Several former GOP rivals such as Ohio Gov. John Kasich, retired neurosurgeon Ben Carson, Sen. Marco RubioMarco Antonio RubioColbert: Students taking action on gun violence 'give me hope' Lawmakers feel pressure on guns Florida lawmaker's aide fired after claiming shooting survivors were 'actors' MORE (Fla.) and New Jersey Gov. Chris Christie could be early contenders.

Trump told The Washington Post on Wednesday that Kasich is "rising rapidly" in his mind, but he threw some cold water on the idea Thursday morning.

"I've had a good relationship with him, and I really got along with him well," Trump told CNBC. "I would say probably it's unlikely that it will be John. I'm not even sure John wants it."