The north London side is struggling in eighth place in the league, and while a win against Reading on Monday could send the club fourth, the team would still be 15 points behind league leader Manchester United.
Despite the criticism of the squad assembled for the 2012-13 season following the departure of captain Robin van Persie, Graham believes Wenger has the ability to attract good players to the club once again.
"There is a lot of hysterical criticism about Wenger now. If you want to stay in the top four, he is the man without question," he told BBC Radio Five Live Sportsweek. "Let's give Arsene the credit. He brought in players for average prices - Thierry Henry, Nicolas Anelka, Marc Overmars, Patrick Vieira, Emmanuel Petit. They were all very good players unknown to the fans in England that he turned into fantastic world-class players. That was his strength.
"He did it on a tight budget so it's not like they are now going to go out and break the transfer record. They have never done it during Arsene's reign so in my opinion he has got to get his magic hat on again and go out and see if he can get players of that quality at good prices."
Graham led Arsenal to league titles in 1989 and 1991, but Wenger is without a trophy in seven years, with the recent Capital One Cup exit to Bradford a particular low for the club in an entirely winnable competition.
However, Graham believes it is up to Wenger as to when he will leave the club, but he has called on the manager to look for better players to give the side a fighting chance of competing for trophies.
"Arsene's first period at the club, for seven years, was probably the most attractive and attacking football I've ever seen in English football," he said. "He won three league titles and four FA Cups. He set the standard and unfortunately in the last few seasons the standard is just slowly slipping away.
"I think Wenger will stay there. He will make the decision if he leaves or not. I cannot see him leaving at all. I think Arsene will still be there for a few years yet. I just hope they bring in a better quality of player."