Photos shared by local media show copies of the Islamic holy book in three toilet bowls.
Campus police say the case is "strange" and "very unusual" due to the religious and ethnic diversity at the school.
Police are trying to identify one of six people seen entering the toilet on the evening of the incident, 28 March.
Investigators have been reviewing security footage to find a suspect.
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A reflection room where multi-faith prayer books are kept on the building's ground floor was not touched, according to investigators.
Police Chief Larry Zacharias told the Dallas Morning News: "No one knows who owns the books, so that makes it difficult."
Mohammad Syed, president of the college's Muslim Student Association, told local media the case was "definitely saddening and a little disturbing as well".
"While there is a little voice of hate, there is an overwhelming voice of love and support and we definitely appreciate that," he said.
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He added that the university is "a very welcoming environment".
The Korans were discovered by members of the student government after an evening meeting.
"I was appalled," said Jonathan Schuler, who found the sacred texts in the toilets.
"It made a lot of the hate I had been hearing and seeing on national news real, and very present."
The student senators have released a statement calling it an isolated incident that does not represent the university community.
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Police are investigating after copies of the Koran were found in toilets in the student union building of the University of Texas at Dallas.