Shares of Gateway rose 12 percent to $1.93 in pre-market trading after the news.
China-born entrepreneur Hui sold low-cost PC maker eMachines to larger rival Gateway in early 2004 for about $290 million in cash and stock. He is now Gateway's second-largest shareholder, behind company founder Ted Waitt, and has previously expressed interest in buying Gateway and taking it private.
Hui, who now owns office-products development firm Joui International, said in a letter to Gateway Chairman Rick Snyder that in order to effectively compete, Gateway must separate its retail operations from its other businesses, as well as make other changes to improve margins.
"I am very disappointed that Gateway has chosen not to constructively engage in discussions with me and my advisors on the proposal that I sent to you on Aug. 3," Hui wrote in a letter dated Monday. "I believe that management and the board need to adopt a sense of urgency to address Gateway's problems."
"The landscape of the PC business has continued to evolve rapidly and Gateway has not reacted. Gateway's stock price has continued to decline and the failure to name a replacement CEO for over six months has left Gateway in a position where it is unable to clearly and credibly articulate its strategic direction to the market," he wrote.
Hui also said he would consider acquiring all Gateway shares and separating the businesses himself, if Gateway prefers that route.
Gateway said its board will review Hui's bid with the help of its financial and legal advisers.
Gateway shares closed Tuesday at $1.72 on the New York Stock Exchange. Last fall, the stock traded at a 52-week high of $3.25, but has since steadily declined to hit a year-low of $1.30 earlier this month. Shares are down 34 percent since the beginning of the year.