"The party has to unite around him," Quayle told CNN's Jamie Gangel in an interview airing Thursday, predicting nevertheless that "holdouts" would remain. "But by and large, I think the party will rally around him."
Quayle served under President George H.W. Bush, who is not planning to attend the Republican convention that is expected to nominate Trump this summer. Several other prominent Republican standard-bearers, like Mitt Romney and former President George W. Bush, are not endorsing Trump either and are skipping the Cleveland convention.
Yet Quayle is more enthusiastic. The former vice president acknowledged that Democratic frontrunner Hillary Clinton has advantages, but said after many underestimated Trump during the primary season it's clear he would find a way win the general election.
"I totally misjudged his ability to win. But for somebody that has really no experience in politics to be able to start off and to win with a strong field and not even go to the convention -- that he is the presumptive nominee a month before we have our final primaries -- is quite remarkable," Quayle told Gangel. "He's a winner so I'm sure he'll figure it out."
Trump's ability to woo party elders like Quayle will be tested Thursday, when the mogul comes to Washington for a meeting with GOP leadership and House Speaker Paul Ryan, who has pointedly declined so far to endorse him. Ryan maintained that he still has reservations about Trump's principles in an interview with CNN's Jake Tapper last week, and the pair's private conversation Thursday morning has been anticipated all week.
Quayle expressed confidence that Ryan would eventually endorse Trump.
"Paul Ryan, in my view, will support our nominee. There's very little doubt in my mind," Quayle said, adding that Ryan should align himself with the overwhelming majority of House Republicans in backing the future nominee. "He's a team player."
This former vice president also had a few ideas regarding whom the presumptive nominee should choose for his running mate. Quayle called Marco Rubio and John Kasich "important" names, but also floated another.
"Rob Portman, to me, would be an excellent vice president and somebody that should be seriously considered. He's got all the credentials," Quayle said of the senator from Ohio. "He knows government. And he would be a good partner for Donald Trump."