The Scottish Football Association has written to Rangers and Mike Ashley seeking clarification about his intentions for the Championship club.
Ashley, who owns Newcastle United, has in return for him having two representatives on the Ibrox board.
He already owns about 9% of Rangers.
However, he has signed an undertaking with the SFA that he will not acquire more than 10% of the shares or have influence at boardroom level.
Ashley's deal, which was agreed on Saturday, has the option of providing Rangers with further loans. It also stipulates that he could underwrite a future share issue.
However, if that were to happen it could take his stake in Rangers International Football Club plc, currently 8.92%, above the 10% threshold if other investors were not sufficiently attracted to the share offer to commit their money.
Presumably, the SFA will want to examine that scenario and look into whether Ashley having two representatives on the Rangers board amounts to a contravention of their agreement that he would not influence its decisions.
Newcastle play in the Premier League in England, which has no rules on dual ownership, but the Football League does, which would present a problem should Newcastle be relegated.
Uefa would also not allow Newcastle and Rangers to compete in the same European competition if they are effectively owned by the same person.
The English businessman, who owns Sports Direct, has control of Rangers' shirt sales and retail division for the next five years. He does this through Rangers Retail, the company he set up after striking a deal with former Ibrox chief executive Charles Green.
He also owns the naming rights for Ibrox Stadium and, previously, tried to acquire the rights to the Rangers trademark.
Earlier on Monday, Sandy Easdale, chairman of the Rangers football board, welcomed Ashley's loan offer, arguing he could "only see it being a good thing".