WASHINGTON — In seeking to rent space in the 58-floor skyscraper that is President Trump’s home in Manhattan, the Defense Department is continuing a long tradition of finding a place close to the commander in chief for his top military aides — including the ones who carry the “nuclear football” of launch codes that follows the president everywhere.

The Defense Department has regularly paid for space near temporary or part-time presidential residences, including near the Chicago home of President Barack Obama. Before that, the Pentagon placed a heavily secured trailer at the Crawford, Tex., ranch of President George W. Bush.

But it is hard to put a trailer with the nuclear football right outside Trump Tower on Fifth Avenue, officials say. Even so, a move into the Manhattan high-rise raises questions of taxpayer money going directly to Mr. Trump.