Republican US presidential candidate Donald Trump (R) and Indiana Governor Mike Pence (L) wave to the crowd before addressing the crowd during a campaign stop at the Grand Park Events Center in Westfield, Indiana, July 12, 2016. [Photo/VCG]

Pence, who faces a Friday deadline on whether to have his name on the ballot to seek another term as governor, said he was humbled to be considered for Trump's running mate.

"I think he's giving it very careful consideration, and we're humbled to be a part of that," Pence told reporters later. "There are a number of other noteworthy Americans that they are considering, and I'm just honored to be on that list."

Republicans close to the campaign said they believed Trump had narrowed his short list to Pence, Gingrich and Christie.

He has campaigned with all three in recent days as he girds for perhaps the most consequential decision of his campaign ahead of the Nov 8 election.

In a sign of how seriously the campaign is considering Pence, Trump was joined at the governor's residence for breakfast by his daughter Ivanka, son-in-law Jared Kushner and sons Donald Trump Jr. and Eric Trump. Kushner and Trump's children have played important roles in the campaign.

Trump's children met with Christie on Tuesday, a source close to the governor confirmed, describing the meeting as good and saying both parties had an existing relationship and were already friendly.

Trump, who wants an experienced politician to join him on the ticket, campaigned with Pence at a rally on Tuesday night in Westfield, Indiana.