Sports Direct has an 18.9% stake in AIM-listed Goals Soccer, which suspended its shares in March after identifying the errors.
The Sky News report, which came in after markets shut on Tuesday, also added that Sports Direct had set Wednesday as the deadline for Goals Soccer to reconsider its refusal to hire Kroll and had warned the directors of possible further action if they do not.
This would be the latest attempt by Ashley to turn around a business in which he is a stakeholder, and it follows a failed move earlier in the year when he tried to take control of struggling department store chain Debenhams.
Goals Soccer declined to comment on the report, while Sports Direct did not immediately respond to a Reuters request for comment outside of business hours.
(Reporting by Muvija M in Bengaluru; Editing by Maju Samuel)
