Carter has been dissatisfied with Rogers' performance at the NSA during a time that saw major security breaches, including that revealed last month by Booz Allen Hamilton contractor Harold Martin III, who is accused of having orchestrated the largest theft of classified government material.
The Post said there was also a second, previously undisclosed breach that was uncovered in 2015 by an employee of the NSA's Tailored Access Operations. The suspect has been arrested.
Clapper, meanwhile, is seeking a separation of leadership roles at the NSA and US Cyber Command, and wants the NSA to be headed by a civilian.
In his letter to Clapper and Carter, Nunes -- who is from Trump's Republican Party -- defended Rogers, saying he has been "consistently impressed with his leadership and accomplishments."
"His professionalism, expertise and deckplate leadership have been remarkable during an extremely challenging period for NSA. I know other members of Congress hold him in similarly high esteem," Rogers added.
He expressed concern that the Post article may contain "unauthorized disclosures of classified information."
And "any decision to end the dual-hatting relationship between NSA and USCYBERCOM should prompt a further review of NSA's organization," Nunes added.