"Zero chance," the Ohio governor said multiple times during an interview on "CBS This Morning" when asked if a Trump-Kasich ticket would give the GOP the best shot at winning in November.
"Look, I am running for president of the United States, and that's it. If I'm not president — which I think I have an excellent shot to be — I will finish my term as governor and then maybe I will be a co-host on your show. You never know."
Walker similarly dismissed the idea, calling it nearly "breathtaking."
Trump's comments have sparked continued interest in his potential running mate, should he lock up the 1,237 delegates needed to secure the GOP nomination. 
Former New York Mayor Rudy Giuliani laughed off Kasich's dismissal during an appearance Tuesday on CNN's "New Day."
"Everybody says that. They all say that," said Giuliani, who last week indicated he'd vote for Trump in the New York primary.
"I like John a lot. I think John would make a good vice president; I think I would make a good president," Giuliani said, adding he didn't think Kasich could lock up the nomination.