WASHINGTON — Shuffling his second-term Cabinet, President Obama plans to nominate Housing Secretary Shaun Donovan to be budget director and is considering San Antonio Mayor Julian Castro to succeed Donovan, according to people familiar with the selection process.

The moves would raise the profile of two men with close ties to the president. Donovan is an original member of Obama’s Cabinet and is well-liked within the White House, where officials have lauded his work overseeing the government’s response to Hurricane Sandy.

As budget director, he would have significant influence over the administration’s policy and spending priorities.

Castro’s star has been on the rise since Obama picked him to deliver the keynote address at the 2012 Democratic National Convention. The 39-year-old Castro is considered a possible vice presidential pick in 2016.

If Castro is nominated to head the Department of Housing and Urban Development, and is confirmed by the Senate, he would become one of the highest-ranking Hispanic officials in the Obama administration.