Adds background on takeover proposal

By Svea Herbst-Bayliss and Harshita Mary Varghese

May 20 (Reuters) - GameStop GME.N increased its stake in eBay EBAY.O to about 6.6% from around 5%, according to a regulatory filing, the latest step in the videogame retailer's push to buy the e-commerce giant.

"Together, the 25,000 shares of Common Stock beneficially owned directly and the shares of Common Stock underlying Put/Call Pairs constitute approximately 6.55% of the outstanding shares of Common Stock," the filing made by GameStop with the U.S. Securities and Exchange Commission said.

Earlier this month GameStop Chief Executive Officer Ryan Cohen surprised Wall Street with an unsolicited offer to buy eBay for roughly $56 billion.

EBay, which is roughly five times as large as GameStop, rejected the offer, calling the proposal "neither credible nor attractive."

Disappointed but not deterred, Cohen has said in interviews that he was sticking with his plan to try and buy the company and would take the offer directly to shareholders if needed.

By increasing his holdings, he might be laying the groundwork to pursue options like calling a special meeting, analysts said.

A representative for Cohen had no comment beyond the regulatory filing.

EBay's shares jumped 35% this year as it reported strong first-quarter earnings amid a fresh focus on high-growth categories like collectibles. Since Jamie Iannone took over as eBay CEO in 2020 after other activist investors forced his predecessor out, eBay's stock has climbed more than 201%.

GameStop shares are up about 9% this year but have fallen 65% since Cohen took over as chairman in 2021.