Texas Tech University System attorney Ronny Wall wrote in the Tuesday memo to the Texas attorney general that the threat came during a Dec. 20 exchange with James' father, ESPN sports analyst Craig James. The Lubbock Avalanche-Journal obtained a copy of the memo in response to an open records request.
The university fired Leach on Dec. 30, two days after suspending him amid allegations he mistreated Adam James, who was recovering from a concussion. The receiver said Leach twice ordered him to stand for hours while confined in a dark place during practice.
Leach denied the allegations, and responded to his firing with a lawsuit against the university, alleging libel, slander and breach of contract.
The Tech memo said James' father "indicated that litigation could ensue" if Tech didn't investigate Leach "for the improper treatment" of his son.
"The threat did not appear to be an idle threat as the parent expressed genuine concern for the health and well-being of his injured child, as well as other student-athletes," the memo continued.
James spokesman Scott McLaughlin issued a statement late Wednesday saying James never threatened to sue Texas Tech.
"Further, Texas Tech initiated its investigation of its own accord," he said.