The Gunners have been a constant in the Champions League during Wenger's tenure but are in danger of missing out on the top four this season.
Arsenal have won just one of their last five top-flight fixtures and occupy sixth place in the table ahead of the run-in.
The north Londoners' destiny remains in their own hands, courtesy of two games in hand, but Souness is adamant ongoing doubts in regards to whether Wenger will sign a new deal have proven to be detrimental.
"Arsenal usually falter in February or March, then reach the top four with a late run in April and May, but I don't see it happening," he told The Times.
"As long as there are doubts over Arsene Wenger's future, it gives the weak personalities in their squad another excuse,' he added.
The Germany international's contract expires in 2018 and he is believed to want pay parity with the Premier League's top earners to stay put.