"I respectfully request that the Durham Report be made available for every Senator to review in the proper setting as soon as possible," Flake wrote in the letter on Thursday.
In 2005, the CIA destroyed videotapes exposing interrogations of terror suspects in a secret prison in Thailand. The Justice Department launched a probe into this matter three years later and issued the Durham Report upon its conclusion.
Flake stressed in the letter senators should be able to examine the document before casting a vote on Haspel's nomination.
During her Senate hearing on Wednesday, Haspel promised that the so-called detention and interrogation program would not resume under her leadership. She has been accused of having allowed waterboarding when she managed the Thai "black site" in 2002.
The Senate Intelligence Committee is expected to vote on Haspel's nomination next week.