State Treasurer-elect Don Stenberg said he'll decide later whether to enter the 2012 Senate race.
"We need a new direction in America," he said in a written statement. "To do that, we need to replace Sen. Ben Nelson in 2012.
"If I become convinced that I am the best Republican leader in Nebraska to go to Washington to help take our country back, then I will run."
Attorney General Jon Bruning announced last week he will seek the Republican nomination for the Senate seat. His announcement followed Republican Gov. Dave Heineman's decision not to enter the race.
Stenberg, a Republican, was defeated by Nelson, a Democrat, for the Senate seat in 2000.
Nelson has indicated he plans to seek re-election.