Correction: An earlier version of this story incorrectly stated that the administration may have to make $35 million in cuts to address a projected shortfall. The figure is expected to be $98 million in cuts. This version has been updated.

The Fairfax County School Board may consider creating new internal audit positions as the administration seeks to operate more efficiently and address a projected $132 million shortfall next year.

In a work session Monday, the board’s Audit Committee recommended immediately hiring at least two people to serve in capacities similar to an inspector general or an independent auditor. Those in the possible new positions, one senior and one junior, would report to the School Board and be responsible for improving the administration’s efficiency and effectiveness. “This issue has been festering for years,” said the board’s budget chair, Ted Velkoff (At Large). “I’m glad we’re going to be addressing this.”

The school board is in the midst of building the fiscal 2015 budget. The school system’s chief financial officer said the administration’s mid-year budget review found an additional $3.5 million in leftover funds, largely from additional sales tax revenue. That money will be added to about $45 million in leftover funds from last year and used to help balance next year’s budget.

School board member Patty Reed (Providence), who is also vice-chairman of the budget committee, said the administration will seek an increase in the county allotment and a series of cuts to cover a projected $132 million shortfall. Much of that is driven by “unavoidable” costs, Reed said, including $27 million in health-insurance rate increases, $37 million in employee retirement-contribution payments and $25 million in costs related to surging student-enrollment growth. The school system, the 11th largest in the country, has 184,625 students and expects an additional 2,500 to enroll next year.

County supervisors have said they will provide a 2 percent increase to the schools’ coffers, but school leaders say that may not be enough to cover the shortfall.

School officials have said a 2 percent increase in county funds would force the administration to find about $98 million in cuts to programs and could lead to staff layoffs and bigger class sizes.

The supervisors and the school board are exploring new ways to increase revenue in the county, including a possible meals tax in restaurants or a tax on movie, concert and theater tickets.

“We’re going to have to face the issue that if we don’t get an economic pickup, how do we get to funding them at the rate of inflation for enrollment growth,” said Supervisor John C. Cook (R-Braddock).

But it’s increasingly apparent that the county is as strapped as the school system for cash, Reed said. Cook reiterated to Reed the supervisors’ previous position on the county allotment. Reed later detailed the discussion with Cook in an e-mail to Schools Superintendent Karen Garza.

Seeking clarity on funding issues, Reed said she asked Cook last week how much the schools would receive for next year’s budget.

“He said 2 percent,” Reed said. Then she asked what would happen if the schools asked for more than that, including perhaps 4 percent.

“He said we’d get 2 percent,” Reed said. “He said that ‘If you ask for more than 4 percent, I feel your credibility will be in question.’ He said: ‘Let’s be credible. Let’s be realistic. It’s unrealistic to ask for more than that and shows you don’t see the constraints on the county side.’”

Cook confirmed the conversation to The Washington Post and said in an interview that in past years, the school system received an increase in county funds of around 8 percent but that “those days are over.”

Antonio Olivo contributed to this report.