Both are conservative, but couldn’t be more different in style: Gov. John Kasich is charismatic, bold and occasionally brash, his statements sometimes lacking caution. Sen. Rob Portman speaks softly, is a meticulous planner, and rarely makes a mistake in public.

Less than one week after President Barack Obama defeated Republican Mitt Romney in an election that revolved around Ohio, these two Ohio Republicans are being talked about as serious presidential candidates in 2016. If they run, they could provide the most prominent moment for Ohio politics since 1920 when Republican Warren G. Harding of Marion defeated Democrat James Cox of Dayton for the presidency.

“It’s been a long time since we’ve had two legitimate presidential candidates from Ohio, let alone at the same time,’’ said Barry Bennett, a Republican consultant in Washington with ties to Portman. “It might be the Ohio (political) consultant full-employment act.’’

John Brabender, who served as a senior adviser to the Republican presidential campaign of Rick Santorum, said, “They’re different candidates, but both in their own ways are certainly credible.’’

Both, too, have done something that eluded Romney this year: winning a statewide race in Ohio.

So far, Portman and Kasich are not giving many hints publicly. Aides to Portman declined to comment on whether he plans to seek the presidency in 2016, but privately Republican officials acknowledge that Portman — who emerged as a prime Romney surrogate in the final months of this year’s campaign — knows the opportunity to run for president is there.

Kasich has been equally coy. At a news conference in Columbus last week, Kasich told reporters that his “only interest is in being re-elected’’ in 2014. But Alex Fischer, chief executive for the Columbus Partnership, told The Columbus Dispatch that Kasich’s name has surfaced as a potential presidential candidate.

“There’s actually something interesting happening on this in the circles I move in as they analyze … the election,’’ Fischer said. “I’ve heard more people say to me this morning that maybe the answer is right under noses – it’s Gov. Kasich.’’

Portman, 56, a first-term senator who served as budget director and trade representative for former President George W. Bush, was on Romney’s short list for vice president this year. A graduate of Dartmouth College who earned a law degree from the University of Michigan, Portman enhanced his national stature after portraying Obama during Romney’s debate preparations, including the first debate that revived Romney’s campaign.

Kasich, 60, a former chairman of the House budget committee, made a brief stab for the Republican presidential nomination in 2000. Unlike Portman, who grew up in a wealthy Cincinnati family, Kasich is the son of a mail carrier in suburban Pittsburgh who earned a degree at Ohio State University. During his two years as governor, the state’s economy has rebounded and the budget deficit closed.

“They’re both quality candidates,’’ said former Republican congressman David L. Hobson of Springfield. “They’re different in their approach and how they do things. But they are both smart and honorable people.’’

Both also have drawbacks. Portman, while skillful at developing a political message, has often been described as a less-than-inspiring speaker.

By contrast, Kasich can be a powerful public speaker. But at times he has a “ready, fire, aim’’ style, such as last year when he called a police officer an “idiot’’ in a speech after the officer stopped him for a traffic violation. The clip was played endlessly during the run up to the Issue 2 referendum that overturned the state’s collective bargaining law that was championed by Kasich.

“If I were Kasich, I’d be worried more about getting re-elected first,’’ said James Ruvolo, former chairman of the Ohio Democratic Party. “If he takes his eye off the ball in Ohio, he could have a real difficult time running for president.’’

Ruvolo said that together the two Republicans might make one solid presidential contender.

“Rob Portman is a smart guy,’’ he said. “If he can get a charisma makeover before running for president, he might have a chance,’’ adding that Portman “is the smarter of the two and the more serious of the two on the issues. If you transplanted Kasich’s charisma and personality into Portman, that would he a hell of a Republican candidate for president.’’

Portman does not face re-election until 2016, so unlike Kasich, he could run for president without worrying about running for another term in his current job. But said Bennett, “I truly don’t know if Rob wants to be president. When you understand you are living on Southwest Airline planes going to corners of New Hampshire and meeting 12 people at a time, it’s a tough slog.’’

If the two Ohioans run for president, the state would be “back in the center once again of the political stream,’’ according to Hobson. But running for president today is a grueling endurance test in which candidates will compete against such likely Republican contenders as Rep. Paul Ryan, R-Wis., Gov. Chris Christie of New Jersey, and former Florida Gov. Jeb Bush.

None of the Republicans interviewed wanted to choose sides if Kasich and Portman somehow emerged from the pack, but Brabender noted that governors sometimes have an edge on the campaign trail.

Governors get “to tout their experience and say they got this done,” he said. “A senator has to say he was one of 100.’’

Joe Vardon of the Columbus Dispatch and Ellen Jervell of the Washington Bureau contributed to this story.