Mr Whyte bought the club for £1 in 2011 while a large tax liability was in dispute. The club went into administration less than a year later and was eventually liquidated when Her Majesty's Revenue and Customs (HMRC) rejected a Company Voluntary Arrangement over an outstanding tax bill.
Police have carried out a series of searches relating to the purchase of Rangers by Craig Whyte from Sir David Murray.
Charles Green later reformed the club after purchasing its assets from Mr Whyte.
It emerged during the administration process that Mr Whyte paid off an £18 million bank debt by pledging future season ticket sales to finance company Ticketus.
It was confirmed earlier that Mr Whyte has lost a £17.7 million court case with the company and he has been ordered pay back the money to the ticket agency following a hearing at the High Court in London.
Last June, a criminal inquiry was launched into Mr Whyte's takeover when the Crown Office asked Strathclyde Police, now part of national force Police Scotland, to investigate the purchase and the club's subsequent financial management.
It followed a preliminary examination of information passed to police by administrators.
The Police Scotland spokeswoman said: "Officers have carried out a number of searches at addresses in both Scotland and England.
"These searches related to both domestic and business premises. This remains an ongoing investigation, and no further information can be provided at this stage."
Police are also investigating the alleged leaking of confidential information relating to the Rangers tax case. Officers were instructed last month to look into suspicions that private details were released while the club was investigated over its use of Employee Benefit Trusts (EBTs).