Frank told the Los Angeles Times he became worried when Thompson sent several e-mails complaining that classmates sitting near him had made offensive comments to him while he was taking a written exam. In one e-mail, Thompson also accused Frank of taunting him.
"I believe I heard you, Professor Frank, say that I was 'troubled' and 'crazy' among other things," Thompson wrote in one of the e-mails. "My outrage at this situation coupled with the pressure of the very weighted examination dulled my concentration and detracted from my performance."
Frank said he was present during the entire exam and saw nothing to support Thompson's complaints. Several teaching assistants also said they saw nothing unusual, Frank said.
Detectives have been trying to discover a motive for the Thursday attack, in which stunned students watched in horror as blood gushed from the 20-year-old woman's neck. Authorities have said Thompson and the woman, who police haven't identified, were not romantically involved.
Thompson was arrested shortly after the stabbing and booked for investigation of attempted murder. He's in jail on $1 million bail and is scheduled for arraignment on Tuesday.
The family of the stabbing victim said Friday that the 20-year-old woman was expected to recover.
Frank said other professors have reported similar exchanges with Thompson, who complained he was the constant target of taunts from students in dorms, dining areas and the library.
"My concern was in the context of other violent incidents on campuses around the country," Frank said.
But a university official told Frank they couldn't order Thompson to seek psychological services.
UCLA spokeswoman Carol Stogsdill said Saturday that university officials were forbidden by privacy laws from discussing how the school may have reacted to any complaints about Thompson's behavior.