Donald J. Trump, the presumptive Republican presidential nominee, was to meet with Gov. Mike Pence of Indiana on Saturday, according to people briefed on the meeting, adding to speculation that the conservative governor is among the finalists to be Mr. Trump’s running mate.

Mr. Pence, who supported Senator Ted Cruz of Texas in Indiana’s Republican primary, is a first-term governor with strong credentials as a social conservative that could help Mr. Trump placate that wing of the party. He was at the center of a contentious national debate last year over religious freedom laws that critics said would allow businesses to discriminate against gay and lesbian couples.

Mr. Pence has stressed recently that he has not had contact with Mr. Trump’s campaign for several weeks, although one person briefed on the process said that the campaign had started vetting him in recent days.

Asked about the meeting, Mr. Trump’s new communications director, Jason Miller, would only say, “Mr. Trump is meeting with a number of Republican leaders in the run-up to the convention in Cleveland, and he has a good relationship with Governor Pence.”