"I think that's inevitable," Jeff Flake of Arizona told NBC's "Meet the Press."
"There will be one, and that I think he'll receive Republican support, or she will," Flake said in answer to a question of whether he could support a Republican presidential candidate who someday supported same-sex marriage. "So I think that yes, that the answer is yes."
Flake, a Mormon, said he had no intention of changing his own views on marriage.
"I believe that marriage should be between a man and a woman," he said. "I still hold to the traditional definition of marriage."
Mitt Romney, also a Mormon and the party's 2012 presidential nominee, said he opposed same-sex marriage but said states could extend some rights to same-sex partners.
The only sitting GOP senator fully supporting same-sex marriage is Rob Portman of Ohio, who told reporters from Ohio newspapers March 14 he switched his stand after his son told him he is gay.
"It allowed me to think of this issue from a new perspective, and that's of a dad who loves his son a lot and wants him to have the same opportunities that his brother and sister would have -- to have a relationship like Jane and I have had for over 26 years," Portman told the reporters in an interview in his Washington office.
Sen. Lisa Murkowski, R-Alaska, said last week her view on same-sex marriage was "evolving."
"I've got two young sons who, when I ask them and their friends how they feel about gay marriage, kinda give me one of those looks like, 'Gosh, mom, why are you even asking that question?'" Murkowski, a Roman Catholic, was quoted by the Alaska Star as saying Wednesday in response to a question after addressing the local chamber of commerce.
Notable deaths of 2014 [PHOTOS]