Some recent polls suggest President Barack Obama and Republican nominee Mitt Romney were locked in a virtual dead heat in Ohio, where some political analysts say the winner of the state's coveted electoral votes might not be known until all votes are counted.
"It's going to be very close, but yes, I do think that we will know before the end of the night," Kasich said on NBC's "Meet the Press" Sunday.
Kasich, a Republican, predicted the voting might not even be that close.
He said his economic policies had turned Ohio's job picture around, which should bolster Romney.
"Independent voters are trending heavily towards Mitt Romney," Kasich said. "And with those numbers like that, it pretty well assures me we are going to know. And I'm not sure the election is going to be as close as what everybody is talking about today."
Republican Wisconsin Gov. Scott Walker told NBC his state and Ohio had adopted economic policies on taxes and regulations that had proven successful and could be adopted by a Romney administration.
"You've got to have a pro-growth agenda out there," Walker said. "When you do, that will help Washington grow in the right direction, and that will put more people to work."