DIA General Counsel George Peirce said the agency was seeking to expand its powers to help recruit sources of intelligence information, the paper reported.
"This is not about spying on Americans," Peirce was quoted as saying in an interview with the Post.
"We are not asking for the moon.
"We only want to assess their suitability as a source, person to person" and at the same time "protect the ID and safety of our officers."
The CIA and the FBI already had such authority and the DIA needed it "to develop critical leads" because "there is more than enough work for all of us to do", he said.
The legislative proposal has been controversial on Capitol Hill and has drawn criticism from groups concerned with privacy and civil liberties, according to the report.
The House version of the intelligence authorization bill, which passed in June, does not include the provision.
But the Senate intelligence committee approved the new authority for the DIA last week and forwarded it to the Senate Armed Services Committee, which reviews sections related to the Defense Department.