Worthington Group plc, which recently purchased a share of a company owned by the club's former chairman, Craig Whyte, posted the notice on Wednesday.
The allegations relate to the conduct of Green and commercial director Imran Ahmad, it said.
Worthington Group said it uncovered the alleged "information" during its purchase of a 26% stake in Whyte's company Law Financial Ltd.
The group claims Sevco 5088, which bought all of the business and assets of Rangers when the club entered administration last year, is a subsidiary of Law Financial.
Rangers released a statement on Wednesday which said Sevco 5088 is a defunct non-trading company, which is "not an active subsidiary of the Rangers International Football Club".
Green, also in a statement to the London Stock Exchange, announced last week that he was stepping down following controversy over alleged racist comments he made in a newspaper interview and speculation that he had closer links to Whyte than he had first admitted to.
Worthington Group's stock market announcement said: "During the course of the company's due diligence process, relating to its purchase of a stake in Law Financial, information has been discovered relating to the conduct of Mr Charles Green and Mr Imran Ahmad. This has today been reported to the Serious Fraud Office."
Rangers said earlier that "no legal claim has been received by Charles Green, Imran Ahmad or the group" from Whyte, Law Financial or Worthington Group.
No-one was immediately available to comment at the Serious Fraud Office.
- Investment & Company Information
- Craig Whyte
- Imran Ahmad