Will 2016 GOP nominee be a fresh upstart or a 2012 redux candidate?

They may have been “beat like baby seals” in the 2012 Republican primaries, but a little more than a year later, some of those losers are already sounding out their chances to try again in 2016.

Texas Gov. Rick Perry, Rep. Michele Bachmann of Minnesota, former Sen. Rick Santorum of Pennsylvania, former House Speaker Newt Gingrich of Georgia and former Utah Gov. Jon Huntsman Jr. have either not ruled out the possibility or alluded to their interest in another bid.

Ana Navarro, a Republican Party strategist from Florida, said it is “crazy” that these also-rans are toying with a comeback after getting “beat like baby seals” by Mitt Romney in the 2012 race.

“It’s like these folks haven’t read the memo that’s sitting in their inbox,” Ms. Navarro said. “You lost. You got beat, some of you into unrecognizable pulps, by a guy who wasn’t even that good. We want to turn the freaking page.”

Ms. Navarro complimented former Minnesota Gov. Tim Pawlenty for moving on and landing a good job in the business world. “A lot of the others just seem to be partaking in magic mushrooms,” she said.

Those flirting with a redux this year are looking at a vastly tougher field, with several hotshot young senators pondering bids along with a cadre of heavyweight GOP governors and former governors.

These 2012-veteran Republicans, though, could be on the right side of history. Every successful GOP nominee in the past 30 years, with the exception of George W. Bush, was taking at least his second shot at becoming the party’s standard bearer.

California Gov. Ronald Reagan lost against incumbent President Gerald R. Ford in 1976 before winning the nomination in 1980, defeating former CIA director George H.W. Bush, who then went on to win the nomination in 1988, topping Sen. Bob Dole, who would return to capture the nomination in 1996.

Sen. John McCain of Arizona lost the 2000 battle to the younger Mr. Bush, but won it in 2008, topping Mr. Romney, who came back to win the nomination last year.

Longtime Republican strategist John Feehery said that it can be “highly addictive to run for president.”

“It’s like posting pictures on Facebook and hoping you get a hundred likes,” he said. “And it helps with increasing your speaking fees and your book sales.”

One man who has said he is done is Mr. Romney — continuing a modern-day trend of declining to run again after winning his party’s nomination but losing the general election — Mr. Dole, Mr. McCain, and Democrats as Walter Mondale and Michael Dukakis.

For those who are considering a repeat bid, there are varying motives.

“For Perry and Bachmann, this comes more under the column of you ’never say never’ in politics, you always leave the door open a crack because it usually doesn’t hurt you to do so,” said Keith Appell, a GOP strategist. “Santorum won some states, won a bunch of delegates in 2012, and he’s still fairly young, so he absolutely should consider it.”

Since his second-place showing in 2012, Mr. Santorum has established Patriot Voices, an advocacy group, and said he is open to another bid for president.

“I’m making no commitments at this point, but we’re not doing anything inconsistent with running in 2016,” Mr. Santorum told Newsmax.com this year. Mr. Gingrich recently was announced as the new co-host of CNN’s “Crossfire” and has said he doesn’t “rule out” a bid.

Mr. Perry, meanwhile, returned to his gubernatorial post in Texas after seeing his presidential dreams unravel in the wake of such infamous debate stumbles as the “three departments” moment. He now shrugs off the cringe-worthy episode and is said to be interested in another run.

In an appearance over the weekend on “Fox News Sunday,” the governor said running for the White House in 2016 is “an option,” but he said his focus in on the current legislative session in Austin.

And Mrs. Bachmann has announced she will not seek re-election to her House seat — but has not ruled out a presidential run, saying “I’m not taking anything off the table.”