Relegation to a lower league would be a huge blow for one of the biggest names in British football who have won the title in Scotland a record 54 times.
Their rivalry with fellow Glasgow club Celtic has been the central element in the Scottish game for decades.
Rangers' parent company is being liquidated, meaning the new owners need to win the approval of seven other clubs in the 12-team SPL if they are to maintain their status.
Their fate appeared to be sealed on Monday when Aberdeen became the fifth club to say they would vote "No" in a meeting scheduled for July 4.
"I can confirm it is our intention to oppose readmission to the SPL for any Rangers NewCo," Aberdeen Chairman Stewart Milne said in a statement on the club's website .
It is not clear if Rangers would have to start life in the lowly third division or be relegated one notch to Scotland's first division.
"The board is also acutely aware that in making this decision, Hibernian - like other clubs in the SPL - will suffer collateral financial damage at a time of severe economic hardship and uncertainty," it said.
Rangers' name was replaced by an anonymous "Club 12" when the Scottish fixtures were published last week.
"The Crown Office has today instructed Strathclyde Police to conduct a criminal investigation into the acquisition of Rangers Football Club in May 2011 and the subsequent financial management of the club," Scottish prosecutors said in a statement on Monday.
"The investigation into alleged criminality follows a preliminary police examination of information passed to them in February this year by club administrators."
