In a report going to board members next week, finance director Nick Kenton said the forecast gives "significant cause for concern".
However, he said there was time to breakeven by the end of financial year.
Raigmore Hospital in Inverness accounts for £10.5m of the potential projected overspend.
Mr Kenton said "significant effort" was needed to achieve "financial break even" and avoid the potential £15.6m overspend by the end of March next year.
Waiting list initiatives, nursing reviews and the use of medical locums have been identified as causes behind the overspend at Raigmore, the largest hospital in the Highlands.
Board members are due to discuss the matter on Tuesday.
In a statement, the health board said: "The £15.6m overspend is a potential projected figure based on the first three months of the financial year and while the board appreciates that it will take a significant effort to achieve financial breakeven, NHS Highland remains confident that there is sufficient time remaining in the financial year to allow the breakeven target to be met."
At the end of the last financial year in April the health board had to ask the Scottish government for a £2m loan to balance its books.

Stephen Kavanagh also said the airline only entered into a pricing arrangement for flying out of the airport.
BIA is suing Aer Lingus for £20m in damages over the switch to George Best Belfast City Airport in 2012.
Proceedings centre on a dispute over the terms of a deal said to have been reached back in June 2007.
It followed months of negotiations as the airline sought to establish a base outside the Republic of Ireland.
Issues under discussion were said to include charging rates and £900,000 in launch support for the three Airbus A320s over the first three years.
According to BIA, the airline then moved its Belfast operation in breach of a binding 10-year contract.
But giving evidence at the hearing on Thursday, Mr Kavanagh rejected that assessment.
Asked about claims his company was under an obligation to stay at Belfast International for 10 years, he replied: "Aer Lingus saw a pricing proposal, based on an initial three aircraft base.
"That was what informed our business case development and analysis, and that is the basis upon which we operated from December 2007 until we left Aldergrove.
"The pricing was adhered to and paid in full."
A barrister for Aer Lingus, further questioned him on a dispute over whether the airline suffered financially from its time at BIA.
"I can be absolute and categorical that Aer Lingus lost a significant amount of money in its operation at Belfast Aldergrove," he responded.
"In terms of our profit, the negative was 44m [euros]. In terms of those costs which directly applied to the operation of the base it was 21m [euros]."
The difference between the two figures was partly based on corporate overheads, he said.
"Without hesitation the operation was loss-making," he said.
"The objective was not just to avoid losses, the objective was to generate a positive return on invested capital.
"So, not only were we far short of breaking even, but we were very much failing in our investment proposition."
The judge was told the situation was in "stark contrast" to other Aer Lingus bases effectively subsidising losses in Belfast.
The airline chief said BIA was made aware of what was happening.
Out of nine routes launched at the airport, five were ultimately cancelled due to the losses, the court heard.
Mr Kavanagh described Aer Lingus's relationship with BIA during the initial years as a partnership both sides were trying to make work.
Referring to talks back in 2007, he said: "The discussions were based on pricing proposals [for] an initial three aircraft base."
The case continues.
NHS Highland has forecast a potential £15.6m overspend based on the first three months of the financial year, but said it expects to break even.
[NEXT_CONCEPT]
Aer Lingus lost up to 44m euros (£32m) from having a base at Belfast International Airport (BIA), its chief executive has told a court.