A report to NHS Dumfries and Galloway seeks approval of its five-year revenue plan up to 2021.
However, it highlights a string of challenges in finding the final Â£2m of savings in an overall target of Â£12.7m.
The board is required to deliver a five-year plan rather than a three-year one due to the major capital investment in a new general hospital in Dumfries.
The report flags up ongoing work to develop "innovative solutions" to find the savings needed to break even in 2016/17.
It stresses that opportunities to make operational savings have diminished to the point that the only viable options are in areas considered very high risk.
At the same time, NHS Dumfries and Galloway is said to be facing other financial pressures including increased prescribing costs.
The future opening of the new district general hospital, which is currently under construction in Dumfries, is also said to carry significant budget risks.
Potential pressure areas include the financial impact of running dual services during the transition process and a potential increase in costs required to meet the staffing requirements of a new clinical care model.
A health board has been warned of an "unprecedented level" of financial risk in trying to meet its savings goals.