The striker, who has become Tottenham Hotspur's talisman over the years, was part of Arsenal's youth academy at the age of eight, but was released before eventually joining their North London rivals at the age of 11.
Kane has gone on to score 100 Premier League goals for Spurs, and his form over the last few seasons has resulted in transfer links to Real Madrid.
While speaking to Corriere della Sera, Brady said: "He was a bit chubby, he wasn't very athletic but we made a mistake. But Tottenham sent him out on loan to lower-division clubs three or four times as well.
"But through his determination he has carved out an amazing career and he deserves it. He has a character that drives him to improve all the time.
"After [Lionel] Messi, [Cristiano] Ronaldo and [Robert] Lewandowski, there is Harry Kane. The statistics speak for themselves and he's still only 24."
Kane scored his seventh goal in as many appearances against Arsenal in Saturday's victory at Wembley.