Ministers are considering setting up the facilities hoped to more relaxed and sympathetic to families than those in sheriff courts where most fatal accident inquiries (FAIs) take place.
The move could also help cut delays in cases getting under way as they would not have to compete for court time.
It would also remove the hearings from any association with criminal proceedings - a key recommendation made by Lord Cullen in a major review of FAIs in 2009. If the plan goes ahead, centres would open in the east, west and the north.
The idea emerged in a Scottish Government consultation document outlining proposals to reform the FAI system published earlier this month. They were introduced in 1895.
It said: "The establishment of such centres would meet Lord Cullen's recommendation that FAIs should be taken out of courtrooms."
It added if the centres were not being used for FAIs, other government business could be carried out on the premises. The proposal follows on from separate wide-ranging reforms in the legal system, including the closure of 10 sheriff courts and the setting up of a dedicated personal injury court.
Patrick McGuire, partner at Glasgow law firm Thompsons, which represents families of victims of work place accidents at FAIs, backed some aspects of the plan. However he added rather than three FAI centres, he thought it better to have one facility within the new specialist personal injury court in Edinburgh, with the possibility of having FAIs there or closer to the family's home in a sheriff court or other building.
He said: "The majority of the cases will involve issues of health and safety as the vast majority of FAIs involve work-related incidents. As the law in this area is extremely complicated it makes sense to have a specialist judge or sheriff presiding too - whether that would be the case at these specialist centres remains to be seen."
He added: "A lot of time, money and effort is about to be made creating the new specialist personal injury court with specialist personal injury sheriffs. These sheriffs will be experts in health and safety legislation so does it not make sense for that to be the place where the vast majority of FAIs take place?"
He said relatives of the deceased should be allowed to decide if the FAI was held at the specialist centre or a court neither their home.
A Scottish Government spokeswoman said: "A consultation on FAI process is ongoing and will run until September 9."