The state wants to build the structure on a lot it owns on Washington Street between 6th and 7th streets.
The 1.6-acre site is being used today as a surface parking lot for state Capitol Mall employees.
The garage would cover the southern half of the lot; surface parking would remain on the northern portion.
In March, lawmakers approved the state spending up to $8 million to build a garage near the Capitol to address a parking shortage.
At the time, state officials said 2,300 state employees in the Capitol Mall have just 1,236 available parking spaces, with a waiting list of 200 names for reserved spaces near the Statehouse.
The parking shortage is magnified during the legislative session, with lawmakers, lobbyists and the public also competing for those spots.
The state reviewed several sites near the Capitol Mall before selecting the Washington Street location.
The Department of Administration said earlier this year that it wants to get the garage built before the Legislature convenes in January 2014.
The Boise Planning and Zoning Commission will hold a public hearing on the project Jan. 7 at 6 p.m. The meeting will take place at the State Capitol via the 8th Street entrance.
Cynthia Sewell: 377-6428, Twitter: @CynthiaSewell