Barnes, who also played for Watford and Charlton Athletic, hopes that Payet remains at West Ham next season, but he has admitted that he would not be surprised if he leaves.
“Once upon a time you would have thought that a player like that who came to West Ham would stay at West Ham but his head could be turned by bigger opportunities,” the former Celtic manager told Guardian-series.co.uk before West Ham’s FA Cup fourth-round tie against Liverpool at Anfield last Saturday evening.
“I like to think not, I like to think he’ll show the loyalty to West Ham to stay, but it wouldn’t surprise me if he doesn’t end up staying.
“For the integrity of football, for someone who has come to the Premier League and been given an opportunity by West Ham, although they paid a lot of money for him and they did well to get him, I’d like to think that he will show some loyalty and stay. But you can never tell.”
Payet joined West Ham from French club Marseille in the summer of 2015 and has taken to the Premier League like a duck to water.
The 28-year-old attacking midfielder has scored six goals and created 61 chances in 17 league appearances for the Hammers so far this season.
The France international attacking midfielder has a pass accuracy of 82% and a shot accuracy of 70%, and has won one header, 45 headers and 11 tackles.
West Ham are sixth in the Premier League table at the moment with 39 points from 24 matches, six points behind Arsenal, who are currently fourth in the standings and occupy the final Champions League spot.