Frenchman Pires was a key figure the last time the Londoners won the top-flight crown, with the 2003-04 'Invincibles' going unbeaten for the entire league campaign.
Arsene Wenger's men had looked to be staging a significant title challenge this term, but three league defeats and two draws in their last seven matches have seen them fall six points behind leaders Chelsea.
With question marks over their ability to live with the leaders - particularly after a 6-0 drubbing by Chelsea last weekend - Pires knows that their home match with City on Saturday is key.
And he believes that anything other than a win will see their title bid come to an end.
"I hope (they can win the title)," he said. "It is my dream for the fans, for the players and for (Arsene) Wenger.
"But it depends on Saturday. If they win they could do it."
That heavy defeat at Stamford Bridge last weekend soured the 1,000th game in charge for Wenger, but Pires - who is currently training regularly with Arsenal's first-team - is adamant that his countryman will be focused on ensuring a response against City.
"Everybody knows Arsene Wenger. He never changes," he added. "He's always the same, like a philosopher with the players.
"After the (Chelsea) game you saw he was upset, but this is normal. He talked with the players on the training pitch on Sunday and they are all focused on Saturday."
While Wenger's own position has come under scrutiny in recent days, one player who has been the subject of some criticism is Mesut Ozil - with the club-record signing failing to match his early promise after his big-money move from Real Madrid last September.
Pires has, however, defended the German and praised his attempts to adjust to Premier League football.
He continued: "Mesut has had a good impact for Arsenal. He's a very good player - maybe one of the best in his position in Europe.
"So for him it's very difficult because the football is totally different in Spain. It's tough (in England) and the tempo is not the same, so maybe he needs one year to adapt.
"I remember my first season was terrible, but after that you play and you learn. I believe in Mesut."
