The company said it was talking to "various parties" about the two-year-old British football blog and its sister sites, which cover individual clubs including Arsenal, Chelsea, Liverpool, Manchester United and Tottenham Hotspur.
Shiny Media managing director Chris Price said the group had found it difficult to make money from the football sites.
Price said: "The revenue side of things has been disappointing. The ad market has been quite challenging. It's frustrating for us because editorially and in terms of community it's very strong, and the brand is very strong.
"We are talking to various parties about selling it. We feel that given the right company, it could be very successful."
The site, which is edited by former Observer Sport Monthly deputy editor Ollie Irish, has stopped publishing new stories, but its archive is still visible.
In his final post for the website, Irish said the decision to call time on Who Ate All The Pies was "very frustrating".
He said: "I won't go into the reasons why -- I'm just the editor, and the decision was not mine -- but fans of the site will be happy to know that Pies may still have a future, so watch the web for more news on that."
Price said that although Shiny had struggled with the low CPM ad rates achievable in sport publishing, its other sectors were buoyant and no other closures were planned.
"We're making money in the other sectors. We are not looking to close anything else," he said.
News of Shiny Media's plans to scale back the sectors in which it operates comes two months after another British blog publisher, Messy Media, closed down its two blogs, political site Westmonster and London lifestyle title Glitterditch.
Shiny Media was set up in 2004 by three freelance journalists, Chris Price, Katie Lee and Ashley Norris, who left the company last month to join an online video start-up.
Norris's parting shot was an opinion piece for news blog TechCrunch in which he argued that British blog publishers had, so far, failed to turn the medium into a successful commercial venture.