In a letter sent to FBI director Robert Mueller, Cornyn said the review's findings "will shed light on what remedial measures the bureau has taken since  to foreclose the possibility of future attacks of this nature."
The shooting spree ended with 29 soldiers wounded and 13 dead in what became the deadliest incident of its kind to happen on a U.S. military base.
During Hassan's military court martial, which is scheduled to restart in August, reports surfaced that the American-born Palestinian had exchanged emails with former Yemeni radical cleric Anwar al-Walaki.
The American-born Awlaki, who was allegedly the spiritual leader of al Qaeda's dangerous Yemeni cell, was killed in an air strike by a U.S. unmanned drone last September. It was the first time the White House approved the targeting and killing of a U.S citizen in a counterterrorism operation.
Despite communicating with al-Waliki while under FBI surveillance, the Justice Department and the Pentagon determined the shootings were not tied to a larger terrorist conspiracy.
Hassan was acting as a lone gunman and not under orders coming from al-Walaki or senior leaders from al Qaeda's Yemen faction, known as al Qaeda in the Arabian Peninsula.
But questions remained over whether the FBI did all it could to possibly prevent the Fort Hood shootings, prompting the bureau's review of the incident and its response.
"We must make it a high priority to ascertain exactly where the system broke down and ensure it does not happen again," according to Cornyn.
The classified report is expected to be delivered to Mueller and FBI leaders on Friday. Cornyn is demanding an unclassified version of the report's findings be disclosed to the public, according to the letter.
"The key findings and recommendations of this report must be made public, so we can glean any and all lessons from this incident," Cornyn wrote.