Dyche's side are seventh in the table as they prepare to host Liverpool, having enjoyed a superb season so far.
On Europe, Barnes said: “Why not? We're seven points clear so why can we not go and challenge the top boys? Every game is tough in this league but we're there for a reason, because we've done so well.
“The league position speaks for itself. We've another tough, tough game now but it's going to be the same for them. Hopefully we can capitalise on that, we're at home so who knows what can happen?
“We've got to believe. Europe's what we're aiming for. If we can get there, then fair play."