The Draper Republican's request comes on the heals of a public skirmish between Jowers and Peter Valcarce, a prominent political consultant who donated $200,000 to the institute.
Valcarce sent a letter to university officials earlier this month, expressing his outrage when he learned that a portion of his money ended up in the Kirk and Kristen Jowers Global Scholarship Fund.
Valcarce went so far as to accuse Jowers of "theft" of the money, demanding the school move the money to the Rob Bishop Civic Engagement Fund, where he said he had intended it to be used.
In a letter last week, the university said it was complying with Valcarce's request to move the money, but expressed its support and confidence in Jowers.
Stephenson said the episode made him start asking questions about the fiscal controls in place in the scholarship funds, and he fears they may be lacking.
"I'm not alleging that trouble exists in any of those vanity funds because I don't even know how many there are," Stephenson said, "but I understand that [Brigham Young University] doesn't allow scholarship funds to be in the name of an existing university official and there are good fiduciary reasons for that."
Holly Braithwaite, a spokeswoman for the Utah System of Higher Education, an umbrella organization for the state colleges and universities, said donations are made from all over, including from faculty and staff, that help thousands of students afford college.
"Of course all donations must comply with federal and state tax laws, and care is taken through financial controls to make sure monies are used appropriately," she said.
Remi Barron, spokesman for the University of Utah, said that "no matter the name of the scholarship, processes are in place to make sure the money is handled properly" and according to the donors' wishes.
Although Stephenson can write a letter requesting an audit, it is up to the Legislature's Audit Subcommittee, made up of legislative leaders from both parties, to prioritize the auditors' workload. That committee won't meet again until next month.