When asked on CNN's "New Day" about being considered an appealing vice presidential candidate, Castro deadpanned: "I hadn't heard that before."
"I'm kidding," he added, cracking a smile.
But the former mayor of San Antonio and Democratic rising star said he was focused on his job in the administration right now -- though he did nothing to rule out the possibility of joining a Clinton 2016 ticket.
"That's very flattering, who wouldn't be flattered to hear that?" he said. "But I have learned in life that the best thing you can do to create a great future for yourself is don't forget what's in front of you. And so I'm trying to do a great job at HUD."
He also sounded very much in Clinton's corner as he defended her handling of a private email server while secretary of state -- an issue seized on by Republicans in the race and in Congress. The Justice Department also is investigating whether classified information was improperly communicated over the nonclassified server.
Speaking from New Orleans, where he is marking the anniversary of Hurricane Katrina, Castro said he stands by his previous statements calling the email investigation a witch hunt.
"If you look at what they're doing on the Oversight Committee, Rep. [Trey] Gowdy and others, the political talk is one thing but what they're doing in Congress in that committee is another," Castro said.
He also echoed Clinton's recently more contrite tone on her decision to use private email while in office.
"I believe that Secretary Clinton has said, has acknowledged that that was not the best way to handle her emails back then ... and has turned over all of the information and the emails and documents and now the server," Castro said. "Folks need to understand that she did not handle classified information that was classified at that the time. It may have become classified later, but it was not classified that way at the time."
Clinton's campaign announced later Friday morning that Rep. Joaquin Castro, Julian Castro's twin brother, will stump for her in Iowa at four events on Sunday. Castro, who is Hispanic, will especially focus on Clinton's immigration policies.