"I'm certainly leaving the door open for that," Santorum told Newsmax.com's "Steve Malzberg Show." "I'm making no commitments at this point, but we're not doing anything inconsistent with running in 2016."
Santorum amassed the second-highest number of delegates in the 2012 Republican primaries and came in third last month in a Conservative Political Action Conference presidential straw poll.
Fourth-place 2012 finisher Gingrich, meanwhile, told reporters on Capitol Hill Thursday he was keeping his options open.
"I don't rule it out, but we're not spending any energy on it," the former House speaker said at a National Review event.
"I would like to be somebody who plays a role in developing a new generation of ideas," Gingrich said, but he acknowledged a new crop of presidential candidates would likely emerge.
Santorum, a former U.S. senator who won 11 GOP primaries last year but lost the primary in his home state of Pennsylvania in a landslide to Mitt Romney, will be 58 years old in 2016.
Gingrich, who carried two primary states and is still seeking to retire nearly $5 million in debt from his 2012 campaign, will be 73 in 2016.
Political parties often nominate candidates who have run and lost before, particularly second-place finishers.
But neither politician is considered a major contender for 2016's GOP nomination, The Washington Post said.
None of the other 2012 GOP hopefuls immediately responded to the Santorum and Gingrich comments.
Other Republican politicians who have expressed an interest in running in 2016 include New Jersey Gov. Chris Christie, Sen. Rand Paul of Kentucky, former Florida Gov. Jeb Bush and 2012 presidential hopeful and former Utah Gov. Jon Huntsman Jr.
On the Democratic side, Vice President Joe Biden, who turns 74 in 2016, has expressed an interest in running and Hillary Clinton, who lost to President Obama in 2008, is being wooed by supporters to run again.
Libertarian Party presidential nominee in 2012 and former Republican New Mexico Gov. Gary Johnson has also said he's interested.