(CNN)John Kasich may not be planning to run for president again in 2020, but he's not ruling out the possibility.
John Kasich on a 2020 run: Never say never
The Axe Files, featuring David Axelrod, is a podcast distributed by CNN and produced at the University of Chicago Institute of Politics.
The two-term Ohio governor noted that his "inclination is to say (he'll) never run for anything again." However, he is maintaining a political organization, planning on forming a team, and won't be waiting on the results of the midterm elections to make up his mind.
"You never want to say never to anything. You never know," Kasich told David Axelrod on "The Axe Files," a podcast from the University of Chicago Institute of Politics and CNN.
Kasich said there is support for him to run again.
"What I have found as I travel around the country for this book or I just travel around period is that people come to me and many of them are just almost begging me to run again," he said.
Kasich sees some of this public desire for him to launch a third bid -- he was a candidate in 2000 as well as 2016 -- as a result of a polarized nation longing for a moderate.
"His supporters are rock solid but they're not a vast number, it's certainly not half the country," Kasich said in reference to President Donald Trump's supporters. "His people may want to take these strong positions, but these polls indicate that everybody would like to see people get along better."
After dropping out of the 2016 race, Kasich was not shy about his lack of support for then-candidate Trump, even writing in Sen. John McCain's name on the general election ballot. Looking back, he told Axelrod that there are still parts of Trump's victory that he doesn't comprehend.
"If I said some of the things he said, I would've been run out of Ohio," Kasich said. "I cannot explain it, I don't understand how people looked the other way and didn't care about some of these incendiary things that and the way that not only him but others behaved."
Nonetheless, Kasich said he is behind Trump.
"I'm going to be for him because he's President. I support presidents and I've always supported presidents but that doesn't mean I go along with them on everything," he said.
As he finishes his term as governor, Kasich said he is focusing on having "an effective voice" -- and indicated it is something that may drive his decision to run for the White House.
"When you're talking about complicated issues like North Korea or you're talking about health care or you're talking about any of these things, you just don't want to talk. You want to know what you're talking about," Kasich said.
"The question is -- and I've thought about this -- is can you be an important voice without holding public office?" he continued. "I think it's extremely difficult to maintain a voice if you're not holding an office."