The Gunners went through the entire campaign without losing a match six years ago, winning 26 and drawing 12 before finishing 11 points ahead of closest challengers Chelsea.
Arsene Wenger's side looked out of the title race earlier this season but they now sit just two points behind leaders Manchester United with nine games to go. Chelsea are on the same points as Arsenal having played a game less.
Eyes on the prize: Clichy is desperate to claim another Premier League medal
When asked if coming out on top would match 2004, Clichy said: 'Even more, because people really doubt Arsenal. With the young team we have, people were saying a lot of bad things about us.
'That is the first thing we want to do. We want to show them we are a bit more mature now and that we can compete in this league, which is the best league in the world.
'We are going to fight until the end to make something happen because this year could be our year.'
Enlarge Top Gunners: Arsenal players celebrate winning the title in 2004
Clichy also claimed he knew it was just a matter of time before striker Nicklas Bendtner found his scoring touch.
The Dane was guilty of missing a host of chances in last weekend's win over Burnley but he quickly answered his critics by demolishing Porto in midweek with a hat-trick in a 5-0 victory.
Clichy added: 'That says everything for the character of Nicklas. Sometimes people can feel he is a bit arrogant and he is a bit careless about the result and what he is doing on the pitch. But he is a great guy and certainly not missing any confidence about himself.'
Hitting the heights: Bendtner was at his best in the Champions League
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