Marshall was the first black to be named to the U.S. Supreme Court and a Baltimore native.
The Maryland House has already approved the legislation, the Baltimore Sun said Friday, but may have difficulty getting it to Gov. Bob Ehrlich's desk because state Senate President Mike Miller opposes the measure.
Miller said he worries that tampering with a name known to millions of passengers around the world could damage a valuable economic asset at a time of growing competition with the region's two other airports, Washington-Dulles International and Washington Ronald Reagan National Airport.
Fiscal analysts estimated the cost to change BWI's name would be as much as $2.1 million in the fiscal year that begins July 1, because the state would assume responsibility for signs at the airport as well as for road signs and other incidentals.