The talented winger has handed in a transfer request to leave Selhurst Park, with Everton his likely destination.
But Barnes believes other clubs will not allow Zaha to play as freely as he does with the Eagles.
"I don't feel Zaha fits into any team, I think he's a bit of a maverick," Barnes told bonusbets.com.
"He does what he does and plays by himself, not in a team. He likes to dribble around five defenders.
"Therefore, he can't go to Man City and Liverpool; he can't go wandering all over the field. He plays whatever position he wants for Crystal Palace and picks up the ball on the right and the left – that's not fitting into a team.
He's got great ability and that's why I think Crystal Palace suit him down to the ground because they allow him to do that, he won't be allowed to at another club. I don't think a player of his ilk should be looking to be a Plan B player to come off the bench."