The probe into "alleged criminality" was instructed by the Crown Office eight months ago following information received from former club administrators Duff & Phelps.
Strathclyde Police refused to discuss reports they think a crime was committed.
Instead they have said: "Police inquiries into the acquisition of Glasgow Rangers Football Club and subsequent management are ongoing and it would be inappropriate to comment further at this time."
Whyte has said he is confident any probe into his time in charge at Ibrox will find no wrongdoing.
A year after the company that ran Rangers went into administration, Whyte said that he would happily co-operate with any investigation looking into his takeover and the subsequent insolvency.
The police are expected to look into whether Whyte ran up debts while the club was effectively insolvent.
Whyte put the club into administration on February 14, 2012.
They are also expected to examine whether the deal that saw Sir David Murray sell the club to Whyte for £1 in May last year was legal.
Before he was confirmed as owner, Whyte set up a deal to complete the purchase of the club by selling off the rights to four years of Rangers season tickets to London-based agency Ticketus to raise £25m.
Most of that was used to pay off the club's debt with Lloyds Banking Group, a condition of the club sale.
Court papers show the administrators' legal advisers told Court of Session judge Lord Hodge they believed the Ticketus deal was illegal on the grounds it was indirectly providing financial assistance for the acquisition of Rangers's shares, contrary to the Companies Act 2006.