West Ham United face a defining run of games in their season in the coming weeks.
The Hammers have enjoyed a brilliant start to the campaign and they currently sit just four points away from the Champions League spaces, meaning expectations have risen considerably at the Boleyn Ground.
However, although Keown acknowledges how well they have done to even get this far, the former Arsenal defender doesn't believe their story will have a fairytale ending.
"West Ham, they have done brilliantly but I suspect they won’t make it," he said. "Big Sam talks about the 40-point safety barrier but they have had to readjust their aims this year and will feel they are not that far away."
West Ham's season is set to be defined over the next few weeks, due to their fixture schedule, and they have a good chance to prove Keown wrong.
They take on Hull City this weekend, a game which they will be favourites for, before having to play Liverpool, Manchester United, Southampton and Tottenham Hotspur in consecutive weeks.
If the Hammers can pick up a considerable amount of points in those matches it is likely that they will be amongst the leading candidates for Europe, but should they fail to impress, their hopes of making it into the top four will have been extinguished.