Wenger has come under fire for his reluctance to spend big and address the ongoing goalkeeping situation at Emirates Stadium, after the erratic performances of Lukasz Fabianski and Manuel Almunia in recent seasons.
But Wilson claims that Wenger was desperate to sign an experienced custudian last summer, only to lose out on his number one target - Pepe Reina.
"Arsene tried like mad to buy not only a goalkeeper, but what he considered to be the most consistent in the country. So he made a big bid for Pepe Reina," the former Arsenal 'keeper told Keys & Gray on talkSPORT.
"That didn't come out because that's not Arsene Wenger's way of doing it and it's not Arsenal's way of doing it, but he did attempt to do that."
Reports suggested that Wenger's bid for the Spanish World Cup winner was worth a club record £20 million, but the Frenchman was forced to admit defeat when Liverpool were reluctant to sell one of their key players to a rival club.
Wenger then turned his attentions to Fulham's Mark Schwarzer, but refused to meet the £3 million asking price for the 38-year-old Australian.
Doubts over Fabianski and Almunia have continued to remain following the emergence of young Polish 'keeper Wojceich Szczesny, who Wilson believes to be a gem in the making.
"I think he [Wenger] would have lost, without any doubt, the young kid Szczesny [had he signed Reina], who I believe is going to be the future," added Wilson.
"It’s most unfortunate he has had this injury and in the game that he had it, but I happen to think Szczesny is going to be a great goalkeeper. The boy is ready now - you ask Arsenal fans."
By James Martini
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
