A number of names have been bandied about to replace Wenger, including Hoffenheim boss Julian Nagelsmann.
“The new man is not going to have the power that Wenger had to go into a board meeting and stamp his feet," Souness wrote in his column for The Times.
“Ivan Gazidis, the chief executive, or whoever else is in charge, will not allow them the same sway.
“It's arguably a tougher job than following Fergie at Manchester United was for David [Moyes].
“Fergie retired in 2013 after securing a 13th Premier League title.
“Wenger won't be going out as a winner and Arsenal, who are now 30 points behind Manchester City after Thursday's defeat and languishing outside the top four, have plenty of catching up to do on England's elite when he does leave."