The museum's permanent exhibition, the Story of North Carolina, relates the state's history from prehistoric days through the civil rights struggles of the 1960s.
"Even with a 20,000-square-foot exhibit, there isn't enough space to continue the last 50 years of history," museum director Ken Howard.
State lawmakers approved a study last year to explore the best way to expand the 20-year-old building, which stretches across the block between the State Capitol and the Legislative Building.
The three main options are adding a floor and expanding along Jones Street, using a parking lot across Wilmington Street for an addition or moving out of downtown and building a new museum on state-owned land near the North Carolina Museum of Art on Blue Ridge Road.
"It would put us right across from the art museum and give us that synergy that we now enjoy with the natural sciences museum," Howard said of the last option.
The North Carolina Museum of Natural Sciences, located across Bicentennial Mall from the history museum, got its own addition in 2012 with the Nature Research Center, while the art museum opened a new gallery building in 2010.
Howard said the history museum is next in line for an expansion.
"I think we'd like to think at the Museum of History that it's our time," he said.
Officials should have a report by early September about the best option, and the museum would then begin a campaign to raise private and public money, he said, noting that it would be five or six years before any project begins.