Gunners manager Wenger has come under increased pressure after a faltering start to the campaign in the Premier League and a shock Capital One Cup exit at Bradford earlier this week.
Graham, who managed Arsenal to league titles in 1989 and 1991, feels Wenger has to put on his "magic hat" and find the next Thierry Henry and Patrick Vieira, whom he moulded into world-class performers.
Graham told BBC Radio Five Live's Sportsweek programme: "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 added: "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 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."
Graham is adamant Wenger is likely to extend his 16 years at Arsenal by several more seasons despite the current criticism.
He said: "Management is about being successful and when you are, you take all the plaudits and the compliments.
"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.
"I think Wenger will stay there. He is very powerful at the club and rightly so.
"He will make the decision if he leaves or not. I cannot see him leaving at all.
"He enjoys Arsenal, the power and influence he has got throughout the club. I think Arsene will still be there for a few years yet.
"I just hope they bring in a better quality of player."
Former Arsenal goalkeeper and ex-goalkeeping coach Bob Wilson has hit back at comments from former player Stewart Robson, who described Wenger as "a dictator in many ways".
There have been reports that Wenger's number two, Steve Bould, has been effectively isolated.
Wilson said: "The claims of Arsene being a dictator, and from a former player in Stewart Robson, really upsets me.
"I believe if Steve Bould is being sidelined, he is wealthy enough, sensible enough and strong enough to resign if unhappy with his role.
"To say Wenger appoints yes men is an insult to all the people who have worked under him - myself included. I always stood up to Arsene."