Story highlights "That's just not going to happen," Booker said

Clinton gave a voluntary interview Saturday about her email arrangements

Washington (CNN) New Jersey Sen. Cory Booker is now referring questions about whether he is being vetted as a potential running mate for Hillary Clinton to her campaign -- a shift from as recently as two weeks ago, when he flatly denied he was in the running for the job.

"I'm just referring questions about the vice presidency to the woman who is going to have to make this decision," Booker told CNN's Brianna Keilar in an interview that aired Sunday on "State of the Union." "You should talk to the Clinton campaign."

Booker's tightly guarded answer is a marked difference from how he responded to that question last month, when he told MSNBC's Andrea Mitchell: "I'm not being vetted."

Booker is one of several Democrats believed to be under consideration by Clinton. Sen. Tim Kaine of Virginia, Sen. Elizabeth Warren of Massachusetts, Housing and Urban Development Secretary Julian Castro, Labor Secretary Tom Perez, Sen. Sherrod Brown of Ohio and Rep. Xavier Beccera of California have all been floated as potential choices.

One factor that potentially could work against Booker is that he's from a state with a Republican governor, meaning his seat in the Senate would almost certainly be replaced by a Republican were he to be elected vice president.

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