The Liverpool legend – a title winner with the Reds in 1988 and 1990 – reckons the Uruguayan has become more liability than match-winner since he made it clear he wants out.
And Barnes has laid it on the line to Liverpool owner John Henry, telling the American to cash in on the striker.
Barnes said: “If Suarez wants to go then you can’t keep him.
“If he’s not going to perform and if he’s going to be disruptive, then what is the point in having him around?
“I like Suarez as a player. But I like Liverpool Football Club more.
“And what’s more important for Liverpool – the club or the player?
“In the past great men have moved on – Kenny Dalglish, Kevin Keegan, Ian Rush – and the club continued.
“If someone like Dalglish wanted to go, the fans would not have backed Kenny. They would have said, ‘Get out of our club because the club is more important than you’.
“In modern-day football the club always must come first. Barcelona is the perfect example of this.
“Even if you are Lionel Messi, the best player in the world, you have a respect, a humility to the club, to the fans, to the Catalan history.
“But the demands of those fans placed on Messi to respect their club, is something we don’t have in England.
“In this country we back players over clubs which makes egos go bigger and, as a result, players are more powerful. The Premier League breeds that kind of greedy, self-centred person.
“That could never happen at Barcelona, or Real Madrid, or Bayern Munich. You have to have that integrity, that respect, that humility. But in the Premier League we don’t have any of that.”
Barnes’ fellow former Liverpool great Graham Souness also believes Suarez, 26, is at the point of no return at the club.