Brady, who made more than 200 appearances for the Gunners between 1973 and 1980 - winning the FA Cup in 1979, has praised 21-year-old Wilshere's impact since returning from his lengthy lay-off with ankle and knee injuries.
The 56-year-old former Republic of Ireland midfielder told TalkSPORT: "We were all a bit nervous - it was 18 months (out injured) - but he has improved with every game and his performance against Liverpool was outstanding."
Brady continued: "I think he will be up there with the very, very skilful creative English players. In my time it was Glenn Hoddle, (Paul) Gascoigne came after that and then (Wayne) Rooney and I think Wilshere will be in that mix.
"I think he is leading the (Arsenal) team now, his pace is deceptive. He has a funny running style but he drifts past players, and he's only 22 (sic), he's only going to get better."
Wilshere is expected to claim his seventh England cap in Wednesday's friendly with Brazil, when former Arsenal left-back Ashley Cole is anticipated to make his 100th international appearance, and Brady said of Wilshere: "I think, like Ashley, he's going to go on and play a lot of games for England."
While Wilshere has been praised by Brady, the Irishman, who will leave his role at the club's youth academy in May 2014, believes Wojciech Szczesny must analyse footage of two of his former team-mates to enhance his ability as a goalkeeper.
"I told him, 'Don't go looking for trouble, don't come charging out of the goal'," Brady added.
"I played with two of the very best goalkeepers in Pat Jennings and Dino Zoff. He probably hadn't heard of him but I told him to google them and watch them - they didn't go looking for trouble, they just dealt with the trouble when it arrived."
On his personal future, Brady said: "I'm not going to retire as such, I'm retiring from my role. I want to take things a bit easier, it's a very demanding job and I want to do something else and the club have said there may be another role for me."