Arsenal have dropped down to sixth following back-to-back Premier League defeats to West Brom and Liverpool.
And just one win in their last five league matches leaves them six points adrift of the Champions League spaces.
The Gunners have tended to finish the season strong in previous campaigns to maintain their record of qualifying for Europe's elite competition under Arsene Wenger every year since 1998.
Graeme Souness believes there are "weak personalities" in the Arsenal squad
Graeme Souness doesn't think Arsenal will finish in the top four
But Liverpool legend Souness believes there are too many issues behind the scene at Arsenal to secure Champions League football for next season.
"Arsenal usually falter in February and March, then reach the top four with a late run in April and May, but I don't see it happening after their defeat at West Bromwich Albion," Souness told The Sunday Times.
"As long as there are doubts over Arsène Wenger's future, it gives the weak personalities in their squad another excuse.
Arsenal line-up if Luis Suarez had signed in 2013
Fri, March 24, 2017
Click through the gallery to reveal Arsenal's 2013/14 team if they had signed Luis Suarez
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Click to reveal Arsenal's 2013/14 team if they had signed Luis Suarez
"It's not good for a player to be playing at home under constant pressure because the crowd are not happy."
Arsenal are next in action next Sunday (4pm) when they host Manchester City who are currently seven points above them in the table.