"I'm not going to make a case for myself for VP," Kaine said during an appearance on a call-in show on WRVA.
But the governor did acknowledge that he is short on experience in foreign affairs, the Richmond Times-Dispatch reported.
"I'm an economy and education guy -- that's what governors do," he said.
The show has been called "Ask the Governor." WRVA renamed it "Ask the Future Vice President."
Kaine was an early supporter of Barack Obama, the presumptive Democratic nominee. He is also an elected Democrat in a state that had been comfortably Republican until recently.
Notable deaths of 2014 [PHOTOS]