GameStop CEO Ryan Cohen has pushed back against eBay's rejection of his $56 billion proposal to acquire the online marketplace, intensifying threats of a hostile takeover bid for a deal that was always a long shot.

Cohen wrote to eBay Chair Paul Pressler on Wednesday, criticizing the company for dismissing his unsolicited offer of $125 per share without "engaging on the substance."

Cohen stated that despite his request to meet with eBay's board being denied, he intends to present the offer directly to shareholders.

"(eBay's directors) should not reject a $125 per share proposal without engaging on the substance. The economic logic is clear and public. eBay's own shareholders deserve the chance to evaluate it," Cohen wrote.

As part of the acquisition proposal, GameStop has built a 5% stake in eBay, providing a foothold for a potential hostile takeover.

GameStop, with a market capitalization of $10.3 billion, unveiled an offer earlier this month to acquire eBay—valued at more than four times its size—through a mix of cash and stock.

eBay rejected the half-cash, half-stock offer on Tuesday, calling it "not credible nor attractive." The company expressed concerns about the financing of the deal, the debt level of the combined entity, and GameStop's governance structure and executive incentive plans.

In his correspondence with eBay, Cohen also raised his own concerns about the e-commerce platform's governance and executive compensation. He noted that CEO Jamie Iannone received $144 million in compensation over a six-year tenure, during which eBay's active buyer count declined.

Cohen further pointed out that Iannone has not purchased any eBay shares on the open market during his time as CEO.

In contrast, Cohen claimed he has stemmed losses at GameStop—largely due to his significant personal capital being tied up in the company. "eBay's directors do not own eBay," Cohen wrote. "Under their watch, user count has declined for five consecutive years."

Cohen's sharp retort to eBay's rejection marks the latest development in one of the most unusual takeover sagas in recent years. While many of GameStop's retail investors, inspired by the meme-stock phenomenon, initially cheered the move, the company's stock has fallen 17% since the acquisition intent became public.

eBay's shares closed up 2.4% on Wednesday at $113, giving it a market capitalization of approximately $50 billion.