INDIANAPOLIS -- Gov. Mike Pence called a meeting with presumptive Republican presidential nominee Donald Trump a "privilege" this week.
The New York real estate mogul posted on Twitter that he was "very impressed" during his meeting with Pence and his family.
Nevertheless, Pence has said his sights remain set on Indiana.
"Today, as you can see, I'm running for re-election for governor," Pence said. "The greatest privilege of my life is to serve as governor of the state I love, and we'll let the future take care of itself."
If given the opportunity to run alongside Trump – and if Pence accepted – it would be the first scenario of its kind in Indiana.
Because state law would prohibit Pence from running both for governor and vice president, the choice of a new Republican candidate for governor would be in the hands of the GOP State Central Committee.
"These are people who have proven themselves as Republicans, but they also are folks who are very conscious of the fact they don't want to lose the office," said Andy Downs, director of the Mike Downs Center for Indiana Politics. "So for them, they'll do more than an average voter would, a balancing act between the right ideology, but also the prospects for getting elected."
RTV6 political insider Abdul Hakim-Shabazz says there's a long list of people who could be considered.
"House Speaker Brian Bosma, former Indy Mayor Greg Ballard, you've got Congressman [Todd] Rokita, [Indiana Republican Party] Chairman [Jeff] Cardwell might be possible contenders," Shabazz said.
Trump is scheduled to attend a fundraiser in Indianapolis on July 12 – just days before the deadline to get off Indiana's ballot.
