The Gunners have endured a mixed start to the season but ensured they remain two points behind fourth-placed Tottenham with a 1-0 win over QPR on Saturday.
And Pires, who was part of an Arsenal side which went an entire domestic season unbeaten to lift the title, believes the current crop have enough about them to finish near the summit.
“I see top three for them,” Pires told ZoneMixte.fr.
|GUNNER DO IT
|20/1||Arsenal are 20/1 to win the Premier League title with Bet365|
The 39-year-old also hailed Arsene Wenger’s financial philosophy, believing it will reap rewards once Uefa’s new Financial Fair Play regulations come into play.
He said: “Now, with the fair-play system, Arsenal will be one of the only clean clubs in Europe. When Arsène explains that he wants to qualify in Champions League, he knows that it is an important competition at the economical plan.
“But I understand fans and players who want to win titles. The Premier League, the Cup, even League Cup are important, because it's a means to making a celebration, therefore the words are not the same and I understand that people could be angry.”
Pires went on to dismiss suggestions that the north London club are reluctant to invest in the transfer market, citing the recent arrivals of Santi Cazorla and Olivier Giroud.
He continued: “I think Arsène can spend money. If it was not the case, Cazorla couldn't come, for example.
“Giroud is good. I ask people to be patient with him. It's not easy for Olivier, he has to score goals, in another country, with another language.
“But his second mission is to replace Robin Van Persie, so good luck!
“His relation with Belhanda in Montpellier for example, its the result of work. This kind of relation, he will have with players like Cazorla, Podolski or Walcott, because there are players who play in side and have to give him good pass.
“People have to remember that Thierry Henry didn't score when he arrived. Now he is a legend. Henry was very strong with Bergkamp, i don't know if he could become a great player without him.”