Castro, a rising Latino star in national Democratic politics, would take the place of current HUD Secretary Shaun Donovan, who would move to head the White House Office of Management and Budget, the source said. Both jobs need U.S. Senate confirmation.
An official announcement did not appear imminent. The White House declined comment on the Cabinet reshuffle.
Castro, 39, mayor of the seventh-largest U.S. city, made his national debut in 2012 at the Democratic National Convention in Charlotte, North Carolina, where he was the first Latino to deliver a keynote address.
Julian Castro turned down an offer from Obama after the 2012 election to be nominated as transportation secretary.
Joining the Obama administration in a Cabinet-level position could give Castro the kind of visibility that could help his chances of being picked as the Democrats' vice presidential candidate in 2016.
Democrats are eager to press their advantage with Latino voters at a time when Republicans have stalled Obama's drive for comprehensive immigration reform.
Donovan, 48, has been Obama's HUD secretary since Obama took office in 2009.