The striker declared last week he wanted to leave Anfield.
Barnes told the Daily Star Sunday: "I would like Luis Suarez to stay but if he is not happy and doesn't want to then he's got to go.
"I always tell fans to fall in love with the club not with individual players.
"Yes, I want Luis Suarez to stay. I think he's a great player. Forget what he does off the field - I'm not judging him by that - but if he wants to go, then he should go and fans should accept that."