He said Police Scotland, which comes into effect from April 1, was committed to maintaining it as a public service but to avoid going down the route of privatisation may need to out-source some of its workload.
Mr MacAskill added he was approaching the issue through tri-partite talks with his Irish counterparts: "I think I see similarities. They wish it to remain a public service. They too do not wish to go down the situation that has played out south of the Border.
"We are certainly not going down the direction they have gone with forensics and we would prefer to co-operate with our Irish cousins."
A government spokeswoman said Mr MacAskill had met counterparts from Northern Ireland and the Irish Republic on February 22 to discuss issues including forensic service, where future joint working was agreed.
She added the administration was committed to the retention of a "world class forensic service" and believed this was best achieved by a public forensic service accountable to the new Scottish Police Authority.
A spokeswoman for the Irish Government said: "There is much to be gained from sharing expertise and capacities in order to generate efficiencies and underpin standards, including shared training."
Chief Constable Stephen House said any outside contractor would have to do the same service, better, for less money, while still making a profit. As policing and services become more efficient under the new single force he thought that would be difficult.
Scottish Police Authority convener Vic Emery added: "We should not close our minds to where we can get best value."