The messages - intercepted well before US and British-led allied forces uncovered the horrific death camps in 1945 - provided clues which could have save millions of lives had they been acted upon.
But analysts largely failed to understand the intelligence, which often lacked context, according to the report by Robert Hanyok, a historian with the US National Security Agency who authored the report entitled "Eavesdropping on Hell."
The analysis "suggests that while the evidence was incomplete, gruesome details from coded Nazi messages that Britain intercepted beginning in 1941 could have confirmed and exposed the scope of German genocide well before 1945," according to the Times.
"The analysis suggests that the allies largely failed to understand the information they had, information that might not have given advance warning of the Holocaust, but could have prompted a military response that could have interrupted the deportations or mass exterminations or, at least a propaganda campaign against Nazi atrocities."
Analysts were looking for information about internal security, bombings and prisoners of war rather than potential evidence of war crimes, and they probably would not have understood the gravity of Nazi plans, Hanyok said, according to the Times.
According to the report, while intercepts allowed the British to "monitor" roundups of Jews in Rome in 1943, "allied communications intelligence, by itself, could not have provided an early warning to Allied leaders regarding the nature and scope of the Holocaust."
"There's a narrow window in which intelligence would have played any kind of role," Hanyok was quoted as saying, "but we didn't see what was happening."
The allied intelligence depicted accounts of massacres, deportations and statistics on killings at concentration camps, but the pieces of information often lacked the necessary context, according to the report.
Moreover, a shortage of translators and large case backlogs hampered US and British efforts to sort the evidence, according to the analysis. The efforts were also hurt by reluctance between the US and British governments to share German communications and more pressing military priorities to sift through evidence.
Anti-Semitism may have also played a role by affecting how the intelligence was handled.
"Both President Roosevelt and Prime Minister Churchill were often hampered in their limited efforts to alleviate some of the suffering by the general anti-Semitic sentiment in both nations," the report said, according to the Times.