Grappling with a waterfront development boom that has sparked a parking crisis in the Seaport District, Massport is proceeding with plans for a massive garage that would be built over the Pike and fit approximately 1,700 cars.

The agency is now seeking a firm to design the multilevel garage, which would be built over the structurally reinforced Interstate 90 tunnel as a shared facility for the planned Boston Convention & Exhibition Center headquarters hotel, other Massport development sites and transient parkers. The garage would cost? an estimated $65 million to $75 million.

Parking is “tightening dramatically” in the Seaport District, said Jim Doolin, Massport’s chief development officer. Developments such as Fan Pier, Pier 4 and Seaport Square have replaced thousands of surface parking spaces and will continue to do so.

“(The garage’s) time has come (due to) the pace of development and the need to get out ahead of a collapsing parking supply,” Doolin said.

Massport’s “air rights” garage plan dates to its 1999 master plan for the 50-acre Commonwealth Flats development area, now part of the Innovation District.

The agency would like to start building the garage next year.

The site, now a gravel lot used for Liberty Wharf valet parking, is bounded by World Trade Center Avenue, the Silver Line World Trade Center T station, ?D Street and the Massport Haul Road.

Massport has allocated up to $7 million for the garage design contract.

“We’re expecting these teams to look at a number of alternatives given the key location,” Doolin said. “We’re going to look at different layouts for efficiency … how it meets the street, is there an opportunity for co-development (of commercial space such as retail) — how can it be more than a garage … but still meet the needs of the parking supply we have?” Doolin said.

The garage would have connections for pedestrians and valet parking for the yet-to-built convention center hotel, and connections to Waterside Place and the MBTA Silver Line.