Graham was the Gunners boss who broke the British transfer record for a goalie when signing David Seaman for £1.3million in 1990.
Seaman spent 13 years at Arsenal, a cornerstone of the club's pursuit of honours, and of the resolute defence Wenger inherited in 1996.
Graham's policy was to pay for the best and then let him get on with the job.
Graham told the Sunday Mirror: "Arsene has the money, so why not go and spend £10m or £12m on a real top-quality keeper? I don't really understand why he has not done that.
"I mean, Schwarzer is 37 and that seems to go against Arsene's policy of recruiting players of that age."