The Gunners have turned a corner under new manager Unai Emery over the past four or five weeks following his appointment as Arsene Wenger’s successor in the summer.
Arsenal have eased to victories over West Ham, Cardiff City, Newcastle United and Everton in the Premier League to hoist themselves up to sixth spot in the table.
The north London side edged to a 4-2 win against Vorskla in the Europa League last week to make a winning start to the group stage in Europe’s second tier competition.
Brentford are in seventh place in the Championship ahead of their trip to Arsenal in the League Cup.
Sky Sports pundit Goodman is backing Brentford to force extra time at the Emirates Stadium in the third round on Wednesday night.
“This will probably be the best footballing game of the whole round,” Goodman told Sky Sports.
“I’m a huge fan of what Dean Smith has done at Brentford but they are not the strongest defensively, which you saw at Derby in the Championship at the weekend.
“Arsenal will be strong in attack and I can see a close game here with both teams scoring. It could easily finish as a draw after 90 minutes but I can’t call who would win if it goes to penalties!”
Arsenal finished in sixth place in the Premier League table last term to miss out on a place in the Champions League.
The Gunners added five new players to their squad to improve their depth and quality in the summer following Emery’s appointment.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news