Chelsea have led the way for much of the season and remain six points clear of second-placed Manchester City and a further one point ahead of Arsenal in third.
But Pires believes Arsenal would have been deserved winners this season.
“In my opinion, this year, Arsenal deserved to be champion, and they won’t be far away,” Pires told Perform.
“I think, once more, there will be some little regrets at the end of the season.”
Arsenal are still to face leaders Chelsea at the Emirates on Sunday, April 26, in a match which could be too late for any impact on who is to be crowned champions.
The Gunners are forever compared to the invincible side of 2003/04 and Pires admits its frustrating for so many Arsenal sides to be so close to the same quality.
“It’s tough and frustrating for the fans. Every time, Arsenal is close,” he added.
“It’s because of the important games that you can’t lose, against Chelsea, City and United.
“But this is the difference. Because against the smaller teams, sometimes there is a misstep or an accident.”
Arsenal take on Liverpool on Saturday in a key clash in the race for the top four and the Gunners can go into second with a win.
Is Robert Pires right to claim Arsenal deserve to have won the league this year?