Obama has already rejected the group's recommendation that the director of the NSA and the head of the military's U.S. Cyber command should not be a single official, as it is now.
The President told panel members he had already decided on a military person to replace Gen. Keith Alexander, who currently hold both positions and will retire next Spring, according to Clarke.
In a statement last week, the White House said, "The Administration has decided that keeping the positions of NSA Director and Cyber command together as one, dual-hatted position is the most effect approach to accomplishing both agencies' missions."
Clarke said, "Our recommendation stands."
Officials briefed on the issue said a three-star Navy admiral is likely to be nominated and given a fourth star.
The White House said it has "no personnel announcements to make at this point on General Alexander's successor."
The President created the panel in the wake of the revelations about the NSA from former NSA contractor Edward Snowden. Snowden is living in Russia and considered a fugitive by the United States on espionage charges.
His supporters cite today's recommendations as further vindication of his efforts as a whistleblower.
"How is it that the United States government can prosecute somebody and threaten them with decade in prison after they expose programs which we now know are unconstitutional according to our own courts, and which the president's own advisory board say is extremely dangerous?" said Glenn Greenwald, the former columnist who was first contacted by Snowden and worked with him to break story after story about the NSA. "The only reason these reforms are possible is because we know about them, and the only reason we know about them is because Mr. Snowden courageously came forward and told us about them."
Clarke said nothing in the report gives any justification for Snowden's actions.
"What Mr. Snowden did is treason, was high crimes, and there is nothing in what we say that justifies what he did," said Clarke.