Wilson, who was an integral member of Arsenal's 1971 Double winning side, has claimed Wenger made a 'big' offer for the Anfield stopper.
In demand: Wilson claims the Gunners made an offer for Reina last summer
'Arsene tried like mad last summer to buy not only a goalkeeper, but what he considered the most consistent in this country. So he made a big bid for Pepe Reina,' Wilson told talkSPORT.
Wilson didn't reveal how much Wenger put on the table for the Spaniard, but it's reported the Frenchman offered something in the region of ?20million.
Wilson added: 'That didn't come out because it's not Arsene Wenger's way of doing it - and not Arsenal's way of doing it - but he did attempt to do that.'
In the absence of Wojciech Szczesny and Lukasz Fabianski, who are sidelined through injury, and Manuel Almunia woefully out of form, Wenger was forced to call upon veteran Jens Lehmann on an emergency loan earlier this month.
Back in the fold: Lehmann was on the bench in Arsenal's 2-2 draw at West Brom on Saturday
And Wilson believes the return of the former Germany international could provide Arsenal with the stepping stone to go on and win their first Barclays Premier League title since 2004.
'Jens would be incredible in the dressing room and I do believe he is fit enough to play,' Wilson said.
'For Jens to be within the Arsenal set-up at this crucial run-in time I think it could be terrific. I think he would very quickly get into his shot-stopping, you just do not lose that. You only have to look at Edwin van der Sar.
'I did speak to him about a month ago and he was more or less saying it was time he needed to spend a little bit more time with his family because his life had been football, but he looked incredibly fit.
'He looked no different from when he played with us and we know he's a conscientious animal. And my goodness me what an input he would have in the dressing room, having been part of the Invincibles team.'
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Explore more:People: Jens Lehmann, Bob Wilson, Pepe Reina, Edwin Van Der Sar Places: Liverpool, Germany