The complaint is understood to centre on how information about the former Rangers chairman's use of employee benefit trusts (EBTs) at the club and his firm Murray International Holdings (MIH) was made public.
Professor Peter Watson, of Glasgow law firm Levy and McRae, said: "Sir David regards such information as private and confidential and the publication as unlawful.
"He has asked that this matter is investigated and that anyone found guilty of breaching the law is the subject of prosecution."
As reported by the Evening Times last week, oldco Rangers won their appeal in principle against a bill from tax authorities over their use of EBTs from 2001 to 2010.
Before the verdict, the "big tax case" had been the subject of widespread media coverage.
Details of EBT payments to staff and players had emerged on the internet and in the BBC Scotland documentary, Rangers – The Men Who Sold The Jerseys.
A First Tier Tax Tribunal delivered a majority verdict in favour of the Ibrox club, following a claim by HMRC over the use of EBTs that could have resulted in a tax bill of £75 million.
Two of the three judges accepted Rangers' argument that many of the payments made to players between 2001-10 through EBTs were loans, and therefore not taxable.
Last week, a spokesman from MIH, said: "It is disgraceful that personal information relating to employees and former employees of MIH and its subsidiaries has been banded about in public."
Sir David sold his 85% in Rangers oldco for £1 to Craig Whyte last May.
The Ibrox club were forced to call in the administrators in February over a separate unpaid tax bill accrued during Whyte's tenure, before being consigned to liquidation in the summer.
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