The proposal does not sound like a "terribly good offer" as it would saddle eBay with GameStop's debt, said retail industry analyst Sucharita Kodali from market research firm Forrester.
It makes sense for GameStop because it could lift its valuation by being linked with a larger company like eBay, she told the BBC.
"The truth is, we are not necessarily putting two strong companies together," Kodali added.
Shares in eBay jumped by more than 13% in after-hours trading when news of the potential offer emerged on Friday, while GameStop jumped by around 4%.
Though GameStop has closed many of its stores in recent years, it still has around 1,600 outlets in the US.
Those shops would give eBay a national network for its "live commerce" and other business operations, Cohen said.
Cohen, who became the GameStop boss in 2023, has criticised its slow shift into e-commerce.
Launched in 1995 as a marketplace for hobbyists, eBay now has 136 million users.
During the Covid-19 pandemic, GameStop was at the centre of one of the wildest stock market tales in recent years as the investment influencer Keith Gill, known as Roaring Kitty, helped boost its value.
GameStop's popularity among retail investors during the pandemic helped coin the idea of meme stocks - those that gain attention through sites like Reddit.
Stocks that often became popular were ones that had been heavily bet against by professional investors, such as hedge funds.
As a result some of these shares - which also included cinema chain AMC Entertainment and phonemaker BlackBerry - saw their prices rise and fall sharply in hugely volatile trade.