Donald Trump and family dropped in for a visit Wednesday morning with Indiana Gov. Mike Pence, fueling already heated speculation that the state's conservative chief executive is the presumptive Republican presidential nominee's choice for vice president.

But that didn’t necessarily rule out other short-listers, including former House Speaker Newt Gingrich and New Jersey Gov. Chris Christie. After Trump met with Pence, he met with Gingrich at an Indianapolis hotel, and was set to meet afterward with Alabama Sen. Jeff Sessions. NBC News reported Christie also met with members of Trump’s family on Tuesday. 

Trump, speaking with Fox News’ Bret Baier in Indianapolis, called Pence “amazing” and said he’s narrowing the short-list, without revealing who is left.

“I tell you, Chris Christie is somebody I've liked a long time; he's a total professional. He's a good guy, by the way, a lot of people don't understand that,” Trump said. “But I'm narrowing it down. I mean I'm at three, potentially four. But in my own mind, I probably am thinking about two.”

Hillary Clinton, meanwhile, was thought to still be narrowing her short-list of candidates -- with speculation Wednesday focusing on the possibility of selecting a running mate with extensive military experience.

Trump met with Pence after the two campaigned together Tuesday night. Trump's daughter, Ivanka and her husband, Jared, were among those who visited Pence at his residence on Wednesday.

Pence reportedly is among the final few Trump is considering as a running mate.

“Everyone here is acting as if it is happening and Pence is the pick,” Indiana Republican strategist Pete Seat told FoxNews.com last weekend.

Pence is viewed as a steady conservative who may help calm nervous Republicans who have become jumpy over Trump’s style -- and who may be an effective counter to Trump’s fiery temperament.

Trump told Fox News' Bill O'Reilly Tuesday that he had "a pretty good idea" of his pick.

Still, he challenged reports that he was planning a Friday announcement as fewer people tend to watch the news that day. 

"When I heard I was doing it on Friday, I was saying, I wonder if those people know me very well," Trump said of his campaign staff.

Speculation over who Clinton will pick is more broad. Sources on Tuesday told Fox News that Clinton’s camp was vetting former NATO leader and retired Navy Adm. James G. Stavridis.

The New York Times first reported that the retired four-star admiral and former NATO Supreme Allied Commander, Europe was being vetted, with sources saying Clinton was likely to seek someone with military experience on the short-list.

Others, however, were skeptical about the possibility of picking Stavridis, with the reports seen as a possible counter to Donald Trump’s consideration of retired Lt. Gen. Michael Flynn.

Labor Secretary Tom Perez, Ohio Sen. Sherrod Brown, California Democratic Rep. Xavier Becerra, Virginia Sen. Tim Kaine, Secretary of Housing and Urban Development Julian Castro and Massachusetts Sen. Elizabeth Warren have all been floated as potential VP picks for Clinton.

Fox News’ Jennifer Griffin, Jake Gibson, FoxNews.com’s Joseph Weber, Christopher Snyder and The Associated Press contributed to this report.