With Ashley Cole looking likely to win cap number 100 against Brazil on Wednesday, Brady thinks that the 21-year-old is good enough to reach a similar milestone later in his career.
"I think, like Ashley, Jack Wilshere is going to go on and play a lot of games for England," Brady is quoted as saying by The Mirror.
"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."
Brady won the FA Cup with the Gunners in 1978 before winning Serie A twice with Juventus.