HUD Secretary Julian Castro is already rumored to be on Hillary Clinton's short list for a running mate in 2016, but he isn't saying. Reuters/Joshua Roberts

WASHINGTON -- Could Hillary Clinton pick Julian Castro, the secretary of housing and urban development, to be her running mate? The former San Antonio mayor isn’t saying.

“I’m trying to do a great job here at HUD,” Castro said when asked whether he was being vetted as a possible running mate for the former secretary of state and Democratic front-runner. “I have had the opportunity to meet briefly with Secretary Clinton on a couple of occasions, and that’s the extent of how many times she and I have spoken. So.”

So no real answer there.

Would he want the job? “I’m going to do a great job at HUD and what I have found, like anything in life, that if you do a great job with what is in front of you, your future opens up, whatever that future is,” Castro said on Thursday, speaking to a group of reporters from the National Hispanic Journalist Association. No real answer there either.

Castro’s name has already begun to appear on short lists for potential Democratic vice presidential candidates -- Clinton nomination or not. He's already endorsed Clinton for 2016. To be sure, Clinton actually has to win the nomination before she can pick a running mate, but she is the dominant candidate with little opposition at this point. The speculation about Castro started when he delivered the keynote speech at the Democratic National Convention in 2012, the first Latino to do so. His speech, like the keynote of Illinois Sen. Barack Obama eight years earlier, was widely praised. At that time, he was the mayor of San Antonio and his twin brother Joaquin Castro was running for Congress, a seat he won.

In 2013, Obama named Julian Castro to serve as HUD secretary, widely viewed as a move to build up the resume of the rising Democratic star. The move to Washington only fueled speculation that bigger office awaits him.

Castro, a youthful 40-year-old, could help lock up the Latino vote for the Democrats, who won overwhelming margins in the last two election cycles. The coalition that elected Obama relied heavily on minority voters. And Republicans have admitted that it will be difficult for them to ever win another national election if they can't improve their showing among Latinos.

“My hope is the Latino community will continue to expand its electoral participation,” Castro said. “I expect the Latino community to play a significant, impactful role in 21016 and beyond. And within the bounds of this role, I look forward to being as helpful as possible.”