Napolitano made the proposal during her first official speech to the Board of Regents at UC San Francisco Wednesday this morning.
She has spent a little over a month in her new job visiting many of the system's ten campuses.
Napolitano observed research at the Riverside campus on the olfactory receptors of mosquitoes and fruit flies that could produce a way to protect people from malaria. She also slept in a living laboratory at the Davis campus that is planned to be the largest zero-net energy community in the country.
She took over as the leader of the university system at a time when finances are improving but serious challenges remain, including rising costs for employee salaries and retirement benefits.
After several years of deep cuts, Gov. Jerry Brown signed a state budget this year that boosts funding for UC.
The former Homeland Security secretary wants the system to bring operational costs to a minimum to keep it affordable. She says education needs to be more accessible.
"It's time for this university to come up collaboratively with a better way," Napolitano said. "I want tuition to be as low as possible and I want it to be as predictable as possible."
Napolitano also says she wants community college transfers to be made more efficient, innovations from UC research to hit the market more rapidly, and the system to become a zero-net energy user by 2025.
Since her surprise appointment as the university's 20th president in July, Napolitano has moved to alleviate the concerns of campus activists who feared she would not advocate effectively for immigrants because of her background in Washington and as a former governor of Arizona.
Napolitano has devoted $5 million to provide special counseling and financial aid for students living in the U.S. illegally. Still, several activists spoke in the public comment session Wednesday, demanding she step down.
(The Associated Press contributed to this report)