FAI guideline review over stillborn deaths
The health secretary has said she is looking at ways to extend fatal accident inquiries to include babies who are stillborn.
Shona Robison says she has asked the Crown Office to consider the issue.
Details emerged as she met families whose babies died or suffered harm due to failings at Crosshouse Hospital in Kilmarnock.
Last year a BBC investigation found that six babies died "unnecessarily" at the hospital.
As a result Shona Robison ordered an independent review and promised to meet the parents involved.
She told the BBC that one of the issues discussed was how to improve investigations into stillbirths.
"The law is one route, but that brings difficulties and complexities in other areas of the law," she said.
"There is the option of prosecution guidelines but the Crown Office needs to be given time to look at this."
It is understood that they would look at changing guidelines rather than legislation - because of the complexity surrounding abortion law.
Ms Robison said they also talked about planned new powers for Healthcare Improvement Scotland, which she said would "bring a more open and transparent culture" around the application of dealing with adverse events in maternity wards.
A review into the deaths at Crosshouse Hospital, published in June, called for improvements in training and staffing and better engagement with grieving parents.
The family of Lucas Morton, who died at Crosshouse Hospital in November 2015 following a series of errors, was one of those affected
NHS Ayrshire and Arran gave the family an "unreserved apology" and admitted Lucas's death was "unnecessary".
Following the private meeting at Crosshouse Hospital, the baby's father, Fraser Morton told BBC Scotland he felt aspects of the discussions had been positive.
"We spoke about the lack of legal status for stillborn babies in Scotland," he said.
"Under dated Scots law they have no legal personality and this stops any external scrutiny of the health board.
"The fact that Lucas was designated stillborn all but ruled out any possibility of a fatal accidental inquiry being held into his death."
Following the meeting, a spokesperson for Healthcare Improvement Scotland said it believed the review's findings supported the wishes of the families involved.
She said: "The issues we've found at NHS Ayrshire & Arran are complex, wide ranging and highlighted comprehensively in the report.
"We are monitoring NHS Ayrshire & Arran's progress against the recommendations to ensure that they maximise opportunities to learn from adverse events."
A spokeswoman for the Scottish government said talks are at an "early stage".
She said: "Scottish government officials have held discussions with Crown Office Procurator Fiscal Service regarding the guidance document 'Reporting deaths to the Procurator Fiscal' as it relates to reporting stillbirths with the aim of providing clarity and consistency for families and medical practitioners."
A spokesman for the Crown Office and Procurator Fiscal Service said: "We can confirm that we have had initial discussions with the Scottish government regarding our guidance to doctors on the types of death which should be reported to the procurator fiscal. "