Mikel Arteta’s side have lost four successive home matches and more than half of their league fixtures so far during the 2020-21 season to sit just 15th in the table.
Cole insists much can and will change over the course of the season but says it will already be ‘very difficult’ for Arsenal to climb into the top four.
He told Stats Perform News: ‘Now they can put Europe on the back-burner and start focusing on getting some points, playing better football and improving the league position.
‘They’re up against some top teams in the Premier League so it is going to be difficult for them.
‘But I feel if they can get through this moment and this tough period with some good games, some good results, then you never know.
‘There’s still a long way to go in this season, but when you’re in the bottom half of the table, to get into the top four now, with the quality some of these teams are playing at, then I think it’s going to be very difficult for Arsenal.’
Arteta’s Arsenal face Southampton at the Emirates on Wednesday night and Liverpool legend Mark Lawrenson expects the Saints to leave north London victorious.
He told BBC Sport: ‘Arsenal did not give up against Burnley, even with 10 men, but they are clearly lacking belief at the moment.
‘The Gunners have had plenty of defensive issues in recent years but they were always a team that created plenty of chances. That is no longer the case, and it is a massive problem for them.
‘Southampton, in contrast, are flying right now. It is fabulous to see them doing so well. They will go to Emirates Stadium and think they can win, and rightly so.
‘On current form, if you go through each team you would not swap any of the Saints defenders, midfielders or attackers for any of Arsenal’s at the moment.’