Booker's answer was less definitive than the one he offered to MSNBC's Andrea Mitchell in mid-June. At that time, he said, "It's flattering and everything like that, but I'm not being vetted."
CNN's Brianna Keilar, filling in for Jake Tapper on "State of the Union," noticed the difference. "That is not a no, sir," she responded. "That is not a no."
"That is exactly what it is," Booker replied. "It's telling you if you have a question like that, please direct it to the Clinton campaign."
Booker, 47 and a rising star in the Democratic Party, is seen as someone who could energize the campaign of one of the most familiar figures in American politics.
Keilar seemed to think Booker had revealed a bit more than perhaps he intended.
"I think I may have gotten the answer that I need from that, actually," she said.
Keilar also asked about the vice presidential prospects of another New Jersey politician, Gov. Chris Christie, who is reportedly a contender to join the ticket of presumptive Republican nominee Donald Trump.
"Look, as you know, Chris Christie and I — even though we're in different parties, and I could write a long dissertation on our disagreements — when I was mayor of the largest city in the state and he was governor, we found ways to work together," Booker said. "But, frankly, I don't care who you put with Donald Trump. You're not going to find a good partnership to lead this country."