"Unless I see a fundamental change it's really hard for me to do a merger," Kasich said in his first interview with his home state's media since ending his failed presidential campaign earlier this month. "If the values are not somewhat similar — if the culture is not somewhat similar — it's hard to do a merger."
"If he changes, that's a whole new ballgame," he continued.
Kasich is one of a handful of Republican governors who has yet to throw his support behind the presumptive GOP nominee.
He said that he, his wife, and his teen daughters have been put off by the Manhattan billionaire's "negativity," but he added that he would not vote for Democratic frontrunner Hillary Clinton.
"That's not going to happen," he said.
Kasich also discussed a book he's working on about his unsuccessful presidential bid.
"How can I let an experience like this not be written about?" he said.
See Kasich through his career:
John Kasich through his career
JOHN KASICH: It's going to be 'really hard' to endorse Donald Trump
MT. PLEASANT, SC - FEBRUARY 10: Republican presidential candidate John Kasich talks to an overflow crowd outside of Finn's Brick Oven Pizza February 10, 2016 in Mt. Pleasant, South Carolina. The South Carolina Republican primary will be held Saturday, February 20. (Photo by Sean Rayford/Getty Images)
11/3/95 - Rep. John R. Kasich (R-OH), seated 2nd from left, and Sen. Pete V. Domenici (R-NM) in the dark suit standing, go over their response to President Clinton's radio address just prior to recording the radio broadcast in the Senate studio. Kasich was casually dressed as the House was out of session for the weekend. (Photo by Robert A. Reeder/The Washington Post/Getty Images)
D:\BOB\budget3.tif - slug: NA/BUDGET date: May 2, 1997 photog: Robert A. Reeder TWP The Rotunda of the Capitol description: GOP happy with their signed budget John R. Kasich (R-OH) is having a particularly good time during the GOP announcement of a new budget in the Rotunda of the Capitol. In front of him is Speaker Newt Gingrich. (Photo by Robert A. Reeder/The Washington Post/Getty Images)
P 350430 022 2May99 Manchester, Nh John Kasich (R-Oh), At The First-In-The-Nation Primary Kick-Off Weekend. (Photo By Jonathan Elderfield/Getty Images)
UNITED STATES - FEBRUARY 02: HOUSE ARMED SERVICES--John R. Kasich, R-Ohio, and Duncan Hunter, R-Calif., talk during House Armed Services Committee hearing on the president's fiscal year 2000 defence budget authorization budget request. (Photo by Douglas Graham/Congressional Quarterly/Getty Images)
Former Ohio congressman John Kasich attends the Republican National Convention at the Xcel Energy Center in St. Paul, Minnesota, Wednesday, September 3, 2008. (Photo by Harry E. Walker/MCT/MCT via Getty Images)
WASHINGTON, DC- Dec. 01: Governor-elect John Kasich, R-Ohio, and House Minority Leader John A. Boehner, R-Ohio, during a news conference after their meeting with other Republican members and governors-elect. Boehner is the presumed House Speaker for the 112th Congress. (Photo by Scott J. Ferrell/Congressional Quarterly/Getty Images)
John Kasich, governor of Ohio, speaks during a groundbreaking ceremony for the Cleveland Medical Mart and Convention Center in Cleveland, Ohio, U.S., on Friday, Jan. 14, 2011. The Cleveland Medical Mart and Convention Center will include a 100,000 square foot medical mart and an adjoining convention center with 230,000 square feet of exhibit hall space. The facility is expected to open in September 2013. Photographer: David Maxwell/Bloomberg via Getty Images
COLUMBUS, OH - MARCH 30: Ohio Governor John Kasich works long hours with staff on his new budget proposal at his office, in the Ohio State House office, Columbus, Ohio, Wednesday, March 30, 2011. Newly elected republican Ohio Governor John Kasich is working toward to balancing an Ohio budget in deficit through a budget proposal with extensive budget cuts, spending reform, and changes in labor laws, including restrictions on collective bargaining. (Photo by Melina Mara/ The Washington Post via Getty Images)
US Republican presidential candidate and former Massachusetts Governor Mitt Romney (2nd L) waves alongside Ohio Republican Senator Rob Portman (L) and Ohio Governor John Kasich (R) during a campaign stop at Tom's Ice Cream Bowl in Zanesville, Ohio, on August 14, 2012. AFP PHOTO / Saul LOEB (Photo credit should read SAUL LOEB/AFP/GettyImages)
UNITED STATES - AUGUST 28: Ohio Gov. John Kasich speaks at the 2012 Republican National Convention at the Tampa Bay Times Forum. (Photo By Chris Maddaloni/CQ Roll Call)
COLUMBUS, OHIO - JULY 21: Ohio Governor John Kasich gives his speech announcing his 2016 Presidential candidacy at the Ohio Student Union, at The Ohio State University on July 21, 2015 in Columbus, Ohio. Kasich became the 16th candidate to officially enter the race for the Republican presidential nomination. (Photo by Ty Wright/Getty Images)
CONCORD, NH - FEBRUARY 09: Republican presidential candidate Ohio Governor John Kasich waves to the crowd after speaking at a campaign gathering with supporters upon placing second place in the New Hampshire republican primary on February 9, 2016 in Concord, New Hampshire. Kasich lost the Republican primary to Donald Trump, though he upset fellow Republican governors Chris Christie and former Governor Jeb Bush. (Photo by Andrew Burton/Getty Images)
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Last week, the Ohio governor shot down the prospects of a third-party bid, which came about after a Washington Post story reported that GOP operatives unhappy with Trump's presumptive nomination were looking for a candidate to run as an independent.
The Post reported that 2012 GOP nominee Mitt Romney made an effort to court Kasich for the bid.
"I'm not going do that," Kasich said. "I gave it my best where I am. I just think running third party doesn't feel right. I think it's not constructive."