Barnes, who also played for Watford and Newcastle United, believe that West Ham will end up eighth or ninth.
“West Ham are another team we were all talking about mounting a potential top four challenge, but their loss to Tottenham on Sunday changes that a little,” the former England international wrote on Titanbet.co.uk.
“Slaven Bilic’s team started well by beating Arsenal, Liverpool and Man City away, then beating Chelsea at home, but their last few games have proven they’re not quite up to sustaining a top four challenge and I think they’ll end up finishing around eighth or ninth, which would be great for them.”
West Ham are having a good season, but they do have slowed down a bit.
The Hammers have not won in their last three Premier League matches, but they are still very much within touching distance of the top four.
The London outfit are unlikely to end up in the top four, but finishing fifth or sixth is not entirely out of question.
The long-term injury to Dimitri Payet means that manager Slaven Bilic will have some tinkering to do to the team in the coming weeks.
West Ham are sixth in the Premier League table at the moment with 21 points from 13 matches, just five points behind fourth-place Arsenal.