Presumptive Republican nominee Donald TrumpDonald John TrumpWSJ: Trump ignored advice to confront Putin over indictments Trump hotel charging Sean Spicer ,000 as book party venue Bernie Sanders: Trump 'so tough' on child separations but not on Putin 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 RubioHillicon Valley: Trump's Russia moves demoralize his team | Congress drops effort to block ZTE deal | Rosenstein warns of foreign influence threat | AT&T's latest 5G plans On The Money: Trump 'ready' for tariffs on all 0B in Chinese goods | Trump digs in on Fed criticism | Lawmakers drop plans to challenge Trump ZTE deal Overnight Defense: White House 'not considering' Ukraine referendum | Pompeo hopeful on plans for Putin visit | Measure to block ZTE deal dropped from defense bill 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."