Former psni chief Sir Hugh Orde hopes a special unit probing the Troubles will be able to continue its work.
Sir Hugh left the top job in the PSNI last August, but yesterday backed the work of the force's Historical Enquiries Team (HET).
The unit is reinvestigating murders from the decades of violence and Sir Hugh hopes funding can be found to sustain its efforts.
The former police chief was in Belfast yesterday to accept an honorary degree from the University of Ulster, but his comments come after the PSNI yesterday warned of the impact of cuts to the police budget.
“It would be a shame if it had to stop doing its business, but again, we are in the world of hard choices,” Sir Hugh said.
“It is not right for me to comment on the challenges that the current Chief Constable faces, but if money can be found from a central source to keep that work going, in terms of value for money, if one equates the delivery, and I'm not making a balancing act here, if one looks at the number of people dealt with by the HET, it is small money compared with other methods of resolution.”
The current Chief Constable Matt Baggott has previously defended the work of the HET, but has warned of the financial pressures facing the wider PSNI.
Yesterday senior officers told the Northern Ireland Policing Board at a meeting in its Belfast headquarters that the policing budget could be slashed by £224m over the next four years.
The Department of Justice has asked the police to calculate the potential impact of a 5% and 8% cut to their running costs following last week's Budget by the Chancellor.
The “scenario planning” exercise has estimated the four-year budget would be shorn of £224m at 8% and £147m at 5%. The PSNI currently has an annual budget of £1.2bn. The issue of dealing with the legacy of the Troubles was highlighted by the recent publication of the Saville Inquiry report into Bloody Sunday that cost close to £200m.
The HET has been able to provide families bereaved in the Troubles with an insight into the circumstances of the deaths of their loved ones.
Sir Hugh told the BBC he believed the HET provided answers on the past, but said its work cost less than other methods of inquiry “which are hugely expensive, frankly, because of the legal bill, if nothing else”.
The comments by Sir Hugh, who left the PSNI to become president of the UK's Association of Chief Police Officers, came only days after the Commission for Victims and Survivors told the British and Irish governments they must take urgent action to deal with the fallout from the Troubles.
The three-member panel noted how the Saville Inquiry report had helped heal the wounds of Bloody Sunday, but warned that thousands of other bereaved relatives deserved answers on the loss of their loved ones.
The report said: “Such an agency would review investigations, seek to recover information for families and examine the truth behind a number of events and issues of critical importance to the unionist and nationalist traditions.”
Meanwhile, Sir Hugh yesterday received his honorary degree of Doctor of Laws (LLD) in recognition of his services to policing at a graduation ceremony held in Belfast's Waterfront Hall.