That's according to people familiar with the selection process. They spoke on condition of anonymity because they weren't authorized to discuss the matter by name.
Putting 39-year-old Julian Castro in the Cabinet would raise the profile of the three-term mayor who's been discussed as a possible Democratic vice presidential pick in 2016.
Obama chose Castro to deliver the keynote address at the party's convention two years ago.
If Castro is nominated and is confirmed by the Senate, he would become one of the highest-ranking Hispanic officials in the Obama administration.
The White House and Castro's office aren't confirming that Castro is under consideration for the post.
Castro would succeed Shaun Donovan, a member of Obama's original Cabinet.
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