The changes could help lessen the furor over the NSA's sweeping powers by narrowing the powers given to its director, officials told The Washington Post.
They could also help avoid an excessive amassing of power in one individual with control over two distinctive operations that have fundamentally different missions -- spying and conducting military attacks, the Post said.
NSA officials are to meet soon to discuss the issue. The White House is coordinating what would normally be an internal Defense Department policy matter because of heightened political sensitivities, officials told the newspaper.
NSA Director Gen. Keith Alexander is due to retire in March. He has led the NSA since 2005 and Cyber Command since its full launch in 2010.
The command defends Pentagon networks and attacks adversaries' computers when directed to do so.
No decision about the changes has been made, administration officials said, but some officials are leaning toward ending the "dual hat" role and putting a civilian at the NSA's helm, the Post said.
"You can't take all this heat you've been taking and not do something," an official told the newspaper.
Defense Secretary Chuck Hagel has given the White House an outline of pluses and minuses of both options, the Post said.
National Intelligence Director James Clapper told the administration he thought it was "important to take a thorough look at the possibility of separating the positions" but also said "the dual-hat construct" under Alexander's leadership "has worked well," Clapper spokesman Shawn Turner told the newspaper.
The dual-hat arrangement "was designed to ensure that both organizations complement each other effectively," White House spokeswoman Laura Lucas Magnuson told the Post.
"That said, in consultation with appropriate agencies, we are always looking to ensure we are appropriately postured to address current and future security needs," she said.