Former President Donald Trump's search for a vice president is formally underway, and there's been an increased focus on four candidates, although his shortlist is not yet complete, and the vetting process is continuing.

Florida Sen. Marco Rubio, North Dakota Gov. Doug Burgum, South Carolina Sen. Tim Scott and Ohio Sen. J.D. Vance have received vetting materials and are the candidates most frequently discussed internally by Trump and his campaign, a source familiar with the process said, but added that the former president may still choose another candidate. NBC News first reported a winnowing of the field.

A source close to one contender downplayed the report, and a senior Trump official said of any narrowing of the shortlist, "Anyone who tells you they know who, how or when is a liar unless it's Donald J. Trump."

These four candidates have received vetting documents, including financial background inquiries, as part of the Trump campaign's search process, Republican sources familiar with the vetting said, but others have also received the comprehensive vetting materials: New York Rep. Elise Stefanik, Florida Rep. Byron Donalds, former Housing and Urban Development Secretary Ben Carson and Arkansas Sen. Tom Cotton. However, the list may still grow, and others may also receive the vetting forms.

Burgum is especially well-liked and respected by the Trump campaign. It is not lost on Trump allies and his campaign that the North Dakota governor is the potential running mate who has traveled the most with Trump on the campaign trail. Burgum and his wife have traveled regularly on the former president's campaign plane. He and Vance are also the only two of the four most frequently discussed contenders who also went to Manhattan to attend and support Trump during the "hush money" trial, where he was convicted of falsifying business records related to a payment to buy the silence of adult film star Stormy Daniels.

In:
• J.D. Vance
• Marco Rubio
• Elise Stefanik
• Tim Scott
• Donald Trump