WASHINGTON — Just six blocks from the White House, the FBI’s hulking headquarters overlooking Pennsylvania Avenue has long been the government building everyone loves to hate. The verdict: It’s an ugly, crumbling concrete behemoth, an architectural mishap — all 2.4 million square feet of it.

But in this time of tight budgets, massive deficits and the “fiscal cliff,” the 38-year-old FBI headquarters building has one big thing in its favor.

It sits atop very valuable real estate, an entire city block on America’s Main Street, midway between the U.S. Capitol and the White House. Just how valuable? The General Services Administration intends to find out.

This past week, the agency that oversees all federal buildings issued an invitation to developers: How would you like to build a new headquarters for the FBI in a different location? In exchange, we’ll consider throwing in the J. Edgar Hoover building and the underlying land as part of the transaction....