The idea is also so preliminary that lawmakers can't yet say exactly how a new process would work. In fact, most of those interviewed said the current system run by the White House works well.
Brennan pioneered the current process to determine which targets are dangerous enough to be placed on one of two hit lists for killing or capture one held by the CIA and the other by the military's Joint Special Operations Command. Many of the names on the lists overlap, and the agency that goes after the target depends on where the suspect appears. That process was described in a legal memo made public this week, and the White House shared classified details with select lawmakers.
The new notion is drawing concern from some in Congress who fear special courts would slow down the drone strikes considered by some, including Brennan, as one of the most effective weapons in the war against al-Qaida.
But many lawmakers say an update is needed in the law, passed in 2001 after the Sept. 11 attacks, that gives the president sweeping powers to pursue al-Qaida. They say that al-Qaida has grown far beyond the war zones and technology has improved, too, enabling a Predator drone operator in the United States to track and kill a target thousands of miles away with great accuracy.
In Thursday's hearing, Brennan defended strikes as necessary, saying they are taken only as a "last resort," but he said he had no qualms about the strike that killed U.S. born cleric Anwar al-Awlaki, because of his roles in several terror attacks.
"The decisions that are made are to take action so that we prevent a future action, so we protect American lives," Brennan said. "That is an inherently executive branch function to determine, and the commander in chief ... has the responsibility to protect the welfare, well-being of American citizens.
Still, he said the White House, too, had considered the concept of the special courts, and he said he would be open to discussing it because "American citizens by definition are due much greater due process than anybody else by dint of their citizenship."
The White House did not offer further comment Friday, and the CIA declined to comment.
Brennan said people are never killed by CIA or military strikes if there is a way to capture them.
Feinstein said at Thursday's hearing that she believed the CIA was open with lawmakers about its part of the program.