Strathclyde Police said officers had been instructed to look into suspicions that private details were released in breach of the law.
The former Rangers club known as "Oldco" was investigated last year over its use of Employee Benefit Trusts (EBTs).
The side effectively won the case after a tribunal ruled that some payments made to players through EBTs were taxable but that many of them could be described as loans, as the club had argued.
An appeal has been lodged by Her Majesty's Revenue and Customs (HMRC).
The probe centred on the period 2000-2011, during Sir David Murray`s stewardship of the club.
The former chairman said in November he had instructed legal advisors to submit a complaint to the Crown Office regarding the publication of information relating to his tax affairs.
The firm Levy & McRae said in a statement: "He has asked that this matter is investigated and that anyone found guilty of breaching the law is the subject of prosecution."
A police spokeswoman said on Tuesday: "Following instructions from the Crown Office, an investigation is ongoing into the circumstances surrounding the alleged leaking of confidential information relating to the Rangers tax case.
"It would be inappropriate to comment further at this time."
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