The proposal, drafted by state Sen. Dwite Pedersen of Omaha, would express the Legislature's "profound regret" for the state's role in slavery, the Omaha World-Herald reported.
The resolution would apologize for the "wrongs inflicted by slavery and its aftereffects" and express "deepest sympathies and solemn regrets" to slaves and their descendants, the newspaper said.
"I'm not expecting a whole lot of controversy," Pedersen was quoted as saying. "My greatest ambition in this is to bring to awareness that slavery was here in Nebraska."
If approved, the resolution would make Nebraska the sixth state to apologize for slavery.
Virginia, Maryland, North Carolina, Alabama and New Jersey all approved such resolutions during the past 12 months, the newspaper said.