Argyle appears to want the deal renegotiated or cancelled, according to industry reports.
Toshiba was forced into looking at selling its memory business after racking up significant losses with its nuclear business.
Throughout most of 2017 Toshiba looked sell its memory chip business and in September of last year signed a $18billion deal with a consortium of acquirers led by Bain Capital and which also includes Apple, Dell, Korea's SK Hynix and the Hoya Corporation.
The deal missed a March 31 deadline, while still awaiting Chinese antitrust authority approval and. according to the terms of that agreement, Toshiba is now able to renegotiate or cancel it.
Argyle is suggesting that the memory division could be worth up to $40billion – Foxconn offered $30billion last year - but as yet it hasn’t generated support from other shareholders to force Toshiba to renegotiate or cancel.