The Gunners saw their bid to secure a return to the Champions League fade away in the closing weeks of a promising first season under Unai Emery.
They still have a chance to snatch a spot in the elite European competition by beating Chelsea in the Europa League final on May 29.
But Van Persie still believes they are close to being title contenders as they seek a first top flight crown since their fabled Invincibles season in 2003/04.
"Of course they can, yes, because they're close already, they've been close for so many years," Van Persie told BBC Sport .
"It goes in periods. Now you have Manchester City , who are doing unbelievable. To win back-to-back titles is very special - that shows, really, that you're a proper team.
"But I hope and wish Arsenal all the best to win the title. I know how difficult it is."