Goals from Theo Walcott, Alexis Sanchez, Per Mertesacker and Olivier Giroud handed Arsene Wenger's men a 4-0 victory over Aston Villa at Wembley to record back-to-back FA Cup final wins
Walcott said afterwards that the Gunners are "very close" to winning the Premier League and Brady agrees with the England forward's summation that a league title is firmly within their grasp
"I listened to Theo Walcott's interview and I agree with him (that) we're not that far away," Brady told BBC Radio 5 Live's Sportsweek programme
"Wenger will know that better than anyone and hopefully he'll improve things that bit more in the summer with signings and we really can challenge.
"But I wouldn't put a time scale on Arsene Wenger."
Arsenal finished the recently-completed Premier League season in third place - 12 points behind champions Chelsea - and Brady said they must avoid any more sluggish season starts if they are to challenge for league honours
"You have to consistently get results (to win the Premier League) and I'm afraid the 12 points Chelsea got in front of us happened at the very start of the league," added Brady, who made 307 appearances for the Gunners between 1971 and 1980
"Arsenal had very inconsistent results and just couldn't match Chelsea's winning run and once they got away from everybody they managed the situation very well
"If you look at the results since the turn of the year, if they can replicate that at the start of the season I think we're in for a very exciting time."
Source : PA