The possibility emerged after Justice Secretary Kenny MacAskill hinted the double jeopardy law could be changed to take in retrospective cases.
The idea appears to be in conflict with recommendations made by the Scottish Law Commission earlier this month.
The Commission said any alterations to double jeopardy should only be for the future and older cases should not be reconsidered.
The centuries-old principle prevents anyone who has already been cleared of committing a crime from standing trial for the same crime again.
However, Mr MacAskill last night suggested that Sinclair could come before the courts again.
He told BBC Scotland: “The decision about whether a case should be re-prosecuted and double jeopardy should be overturned will ultimately be a matter for law officers.
“But our view is that the law officers should have the right, and if it is retrospective then so be it. The law officers will have our full support.”
Convicted double killer Angus Sinclair, 62, was accused of raping and murdering Christine Eadie and Helen Scott after they had been on a night out at the World’s End pub in Edinburgh in 1977.
However, the charges were thrown out after the judge upheld a defence argument of insufficient evidence.
Asked whether changes to the law should allow for cases to be looked at retrospectively, a Scottish Government spokesperson said last night: “New legislation is required on this, and required now.
“We want a double jeopardy law which is fit for the 21st century. We want to act swiftly to seek views from the legal profession on this.”
The proposals would bring Scotland into line with alterations made to the law in England and Wales four years ago. Since then, there have been three successful re-prosecutions.
Sinclair is currently serving a life sentence for the murder of Mary Gallacher in 1978 and is suspected of being a serial killer also responsible for the deaths of at least six other women, including Ms Scott and Ms Eadie.
The SLC in its report made no recommendation on whether the clarified law should allow for a retrial if new evidence emerged.
It also recommended the rule should not apply if an acquitted person later admitted carrying out the offence, or in cases where the original trial was corrupted, for example by jury rigging or witnesses being intimidated.
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