The Navy made Cosby an honorary Chief Petty Officer in 2011.
The Defense Secretary denied reports of bad blood with President Obama.
Obama is expected to name former Undersecretary of Defense Ashton Carter to the position.
The Pentagon still needs congressional approval for funding to support vetting and recruiting process of foreign forces, according to Press Secretary RADM Kirby.
According to CNN, Carter and Homeland Security Secretary Jeh Johnson were on the shortlist.
Even as Defense Sec. Hagel’s resignation was met with claims that he was pushed out. Pentagon Press Secretary, Rear Adm. Kirby, said this is false.
Reed’s name had been floated as a potential replacement for current Secretary of Defense Chuck Hagel, who announced his resignation Monday.
Hagel will stay on as Defense Secretary until a successor is approved by the Senate.
The original request was $13.3 billion in March.
The Department of Defense isn’t taking federal sequestration lying down.