A shareholder's complaint over alleged market abuse by the 58-year-old South Africa-based businessman has led the Financial Conduct Authority (FCA) to look into the matter.
The move comes amid growing concerns about the League One champions' finances and governance.
Mr King has said he was not interested in buying existing shares in the operating company Rangers International Football Club plc, but was willing to be a "significant investor" and suggested a brand-new rights issue.
The complaint made to the FCA claimed the board had no intention of dealing with Mr King, who is one of South Africa's wealthiest tycoons.
The Glasgow-born entrepreneur, along with legendary former player Richard Gough, set up Ibrox 1972 Ltd as part of a campaign to withhold fans' season-ticket cash. The campaign launched with the Union of Fans aims to hand over supporters' season-ticket cash once they are given security over Ibrox Stadium.
The club has condemned it as a conduit for depriving it of revenue.
The FCA told the complainant: "We will review the information you have provided very carefully with a view to determining whether it is appropriate to exercise any of our statutory powers in respect to market abuse."
The conduct team can impose unlimited fines and in extreme cases of market abuse can carry out a criminal investigation or hand the case to the Serious Fraud Office.
Any investigation would take into account whether it believes actions were deliberate, whether confidence in the markets was damaged or put at risk and whether there was financial gain.
It would also look at the conduct of the accused person before and after the alleged breach including previous disciplinary action and compliance.
Mr King was unavailable for comment.