The Gunners look set to lose skipper Cesc Fabregas, and most pundits think they are the most likely to drop out of the top four.
But midfielder Ramsey, 20, who will lead out Wales in a friendly with Australia tonight, insists his club are still targeting the title - and every other competition.
He said: "Arsenal have handled those things in the past. Nobody takes too much notice, we know what we have to do.
"There's no question about the ability we've got. We'll still be a force.
"I think we will be there or thereabouts at the end of the season.
"To be honest, we'd like to win everything."