The former defender is worried that the side don't have a natural leader that will stand up and be accountable.
The Gunners are under increased pressure just seven games into the season, having started the campaign slowly compared to the form that they finished 2014/15.
They have also struggled in the Champions League, losing to both Dinamo Zagreb and Olympiakos in their opening group games - contests many believe they should have won comfortably.
Questions are now being asked of Arsene Wenger and his side and what they are lacking, and Winterburn believes leadership is an issue they need to address.
“I think one of Arsenal's problems is that they don't have a natural leader on the pitch who can keep them together,” he told Sky Sports.
“Sometimes someone in that Arsenal team needs to say: ‘Do you know what, I am going to take responsibility for this team.’ It should be that each individual section of the team is doing that but, if not, one player has to stand up and be accountable.”
Is this Arsenal side lacking a natural leader?
When looking at the current members of the Arsenal side, it is clear to see that a lack of leaders may indeed be their problem.
The best Gunners sides from the past all included big personalities that could carry the team, with the likes of Martin Keown and Patrick Vieira principal among them.
Their Premier League rivals all have personalities of that ilk, for example Manchester City have Vincent Kompany, Manchester United have the likes of Bastian Schweinsteiger and Wayne Rooney and Chelsea have John Terry.
Arsenal, though, do not have that defined leader in the side, with the likes of Santi Cazorla or Mesut Ozil unlikely to come out on top in a midfield battle. Rather than a striker, perhaps that is the area Arsene Wenger should look to improve in future.