Newcastle United owner Ashley holds an 8.92 per cent stake in the cash-strapped Scottish Championship club and has an agreement with the SFA that he is unable to raise his holding beyond 10 per cent.
The SFA issued notices of complaint to Rangers and Ashley amid concerns over breaches of dual interest rules and the Glasgow club face a disciplinary hearing next month.
Ashley's holding company, MASH Holdings, sought permission from the governing body to raise its stake in the club, but the SFA have rejected that proposal.
A statement on the SFA website said: "The Scottish FA Board convened on Tuesday, 23rd December to hear a submission from the Board of Rangers Football Club.
"This meeting was arranged in respect of a request set out in an Application to Consent to an increase in MASH Holdings Limited's shareholding in Rangers International Football Club to a maximum of 29.9 per cent of the issued share capital.
"The Board has now carefully considered the Application and has decided, unanimously, that the Application should not be granted.
"The Board, under Article 13 of the Scottish FA Articles of Association, is required to have due regard to the need to promote and safeguard the interests and public profile of association football, its players, spectators and others involved with the game. This test is set out in full in Article 13.6."
Rangers are on the lookout for a new manager after Ally McCoist was put on gardening leave for the last year of his contract having tendered his resignation.
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