The idea was voiced during a Senate committee hearing on the confirmation of John Brennan to be the director of the CIA, The New York Times reported Saturday.
The courts could be similar to the Foreign Intelligence Surveillance Act courts established in 1978 to approve domestic national security surveillance.
During the hearing Thursday, Sen. Ron Wyden, D-Ore., complained the White House would not give him even a list of countries where drone strikes had been conducted, while Sen. Saxby Chambliss, R-Ga., criticized the strikes as substitutes for capturing terrorists.
How the U.S. determines whom drones target became a public question after a drone killed U.S.-born Anwar al-Awlaki, who was a member of al-Qaida in the Arabian Peninsula.
"Having the executive being the prosecutor, the judge, the jury and the executioner all in one is very contrary to the traditions and the laws of this country," said Sen. Angus King, Ind-Maine.
Brennan said the Obama administration had held internal discussions on the issue, which he said was "certainly worthy of discussion."
Experts say such a court probably could not act with the speed that might be required in some rapidly developing situations. Rather, the court might rule on whether there was enough evidence to put a suspect on a kill list.