Wenger has come under pressure from Gunners fans following a difficult start to the season.
"They need experienced, outstanding players and I think they need about another three in the side at the present time," Graham told Radio Five Live's Sportsweek programme.
"They've got the money, let's sit down, get some of these players in he's supposed to be after and let's see if they can start winning trophies again."
The Scot, who led Arsenal to two league titles, claimed it would be "a struggle" for Arsenal to finish in the top four this term.
"They have big signs at the club saying 'Arsene knows'. Well I hope he does," added Graham.
"I think he's going to be there this season. I think he's under a little bit of pressure just now from the fans.
"But I think Arsene, if he sits down and is honest with himself, he'll put it all back together again. But he needs to do some hard thinking.
"Please get the the cheque book out Arsene. I think they need another centre-half, I think they still need a strong, outstanding, experienced midfield and I still think they need an out-and-out striker like a (Thierry) Henry."