Citing the tradition of reserving courthouse lawn space for just veterans, the council suggested the library or a town park as a suitable place to honor the famed orator and author, the Baltimore Sun reported Monday.
The move has enraged supporters of a Douglass memorial.
"We have a Confederate soldier there at the top of a monument that represents the darkest period in American history," said Walter Black, who heads the county's chapter of the National Association for the Advancement of Colored People and is chairman of the county historical society's Douglass project.
But County Councilman Philip Carey Foster, among others, is holding firm to the tradition that reserves the lawn for war memorials. He says talk of balance smacks of "political correctness."
If anything, Foster says, the unwritten rule needs to be formalized to prevent disputes.
Said Foster: "The council is very supportive of a memorial for a man of his prominence, but the lawn is for war memorials. If the goal is to provide a fitting monument, there are alternatives."