May 3 (Reuters) - GameStop proposed on Sunday to buy eBay Inc for about $56 billion in a cash-and-stock deal, with CEO Ryan Cohen saying he was prepared to take the bid directly to shareholders should eBay’s board be unreceptive.

GameStop - once a stock market minnow that shot to fame during a meme-stock frenzy five years ago - is offering to pay $125 a share in a 50-50 mix of cash and stock, Cohen said in a letter to eBay’s board. Based on eBay’s Friday close, the bid represents a premium of about 20%.

EBay has a market capitalization nearly four times larger than GameStop, making the buyout bid an ambitious attempt.

The U.S. videogame retailer has already built up a 5% stake in eBay through shares and derivatives, Cohen said in the letter, which was seen by Reuters.

Its unsolicited offer to buy the U.S. online marketplace was first reported by the Wall Street Journal, citing an interview with CEO Cohen, also GameStop’s largest investor.