eBay has rejected an unsolicited takeover bid from the much smaller US videogame retailer GameStop, calling the $56 billion (£41bn) offer “neither credible nor attractive”.

GameStop chief executive Ryan Cohen had announced the bid last week, saying he would try to acquire the larger company for $125 per share in a cash-and stock deal, but doubts had persisted from the beginning about how GameStop would finance such an arrangement.

eBay has a market valuation of just over $48bn, and has seen its shares rise about 26 percent so far this year, as its chief executive executes a turnaround plan, while GameStop – best known as a “meme stock” promoted on social media, to the detriment of short sellers – is valued at just over $10bn.

Paul Pressler, chair of eBay’s board, said in a letter to GameStop that the board along with independent advisers had “thoroughly reviewed your proposal and has determined to reject it”.

“We have concluded that your proposal is neither credible nor attractive,” Pressler wrote.

The company said concerns around the proposal included the “uncertainty” around its financing, operational risks, and the debt load that the combined company would take on as a result of such a transaction.

Cohen said GameStop had agreed $20bn in financing from TD Securities and had about $9bn on hand, but that left a large remaining gap in funding.

Cohen previously said he would take the deal directly to eBay shareholders if the board rejected his offer.