Richard Hughes, the co-founder of Zeus Capital, which was at the centre of former chief executive Charles Green's takeover in 2012, is believed to have paid 1p each for the shares.
But he is thought to have sold his stake in Rangers International Football Club on Tuesday when some shares were being traded at 24p.
The deal came on the same day that Guernsey-based Damille Investments II Limited bought two million shares in the club, giving it a 3% stake.
Mr Hughes played a pivotal role in the purchase of the assets of the Ibrox club for £5.5m by Mr Green's Sevco consortium after the oldco went into administration in February 2012.
Mr Green stood down from his role as a paid consultant at the club and began to sell his shares in RIFC in August last year, amid continued infighting at boardroom level.
He quit as chief executive in April last year following allegations about his dealings with former owner Craig Whyte and anger over alleged racist comments made about former director Imran Ahmad.
Rangers value on the stock market had been cut by more than half in the past four months amid a battle for power in the Ibrox boardroom.
When Damille bought into RIFC, the share price was down 56% from the 55p reached in September at the height of shareholder disquiet over the administration of the club. The stock market value of RIFC had dipped from £35.8m to £15.6m - its lowest in its first year.
Since the share deal, the share price has risen to finish yesterday at 28.5p.
Mr Hughes became embroiled in an alleged tax scandal in November 2012 when it emerged HMRC was investigating tax schemes set up through his Zeus Partners company. Zeus Partners, which is not connected to Zeus Capital, was alleged to have created and marketed a £134m film investment scheme the taxman suspected was part of an illegal effort to generate millions of pounds in tax relief.
It said at the time that it "categorically denies any wrongdoing".
This article has now been amended to clarify that Damille bought two million shares - not £2m worth.