If the duo paired up, there would be not one but two men on the ticket who have been widely criticized and sometimes mocked for some of their suggested policies.
Here's a review of five of the former House Speaker and former presidential hopeful's most controversial ideas.
Make the Moon America Again
Gingrich has repeatedly spoken about his fascination with outer space and the moon, making it no surprise that some of his most other-worldly suggestions have been based around the subject.
In what even Gingrich said was "the weirdest thing I've ever done," he created a bill while he was a congressman that would allow for a lunar colony to apply for statehood once there were 13,000 residents.
He joked about the bill during the 2012 presidential campaign, but that is just one of several ways that he has incorporated outer space into domestic, and intergalactic, policy.
Traffic Issues Solved by Mirrors on the Moon
Using lights on the country's highways to make nighttime driving safe is so 20th century.
Gingrich proposed installing a mirror system on the face of the moon, the reflections of which would help light the highways and save Earth-bound residents tax dollars.
In a 2011 column about Gingrich, David Brooks of The New York Times wrote that Gingrich suggested such a system "could provide the light equivalent of many full moons."
Bringing Back Orphanages
When he was a congressman from Georgia who was expected to be selected as the House Speaker, Gingrich advocated for taking poor children away from the care of their parents and placing them in orphanages.
Gingrich argued that the move, which was widely slammed for being Dickensian, would save money that would have been spent on welfare.
Bringing Back Child Labor
While the orphanages idea doesn't appear to have been brought back up in roughly two decades, Gingrich has long been a proponent of allowing poor children to work at a younger age than allowed by law.
The prospect of changing child labor laws is one that he addressed as recently as his 2012 presidential bid.
In 2011, he said that child labor laws are "truly stupid." Instead, children should be allowed to work as janitors at their schools.
"These schools should get rid of unionized janitors, have one master janitor, pay local students to take care of the school. The kids would actually do work; they'd have cash; they'd have pride in the schools. They'd begin the process of rising," he said at an event at Harvard's Kennedy School of Government.
The Moon as the Hottest Honeymoon Spot
Gingrich, who is now married to his third wife, predicted that the moon would be the new Hawaii in terms of honeymoon locations come 2020.
In his 1984 book "Window of Opportunity," Gingrich wrote that he thought "honeymoons in space will be the vogue by 2020."
"Imagine weightlessness and its effects and you will understand some of the attractions," he wrote.
Despite recent advances by private space companies such as SpaceX and Virgin Galactic, space tourism doesn't appear to be in the cards any time soon. But he's still got four years to turn the trends around.