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The Gunners entered the international break with an eight-point lead over Pep Guardiola's defending champions, who have a game in hand, and are just 10 games away from clinching glory.
A tough month lies ahead for Arsenal in April, with trips to face Liverpool and City as well as a home clash with Chelsea, while high-flying Newcastle United await in May.
Arsenal has fallen short in its quest to end its Premier League trophy drought and the side's inexperience in such situations raises concern, though former captain Van Persie sees no such issues.
"Arsenal are doing really well, they play consistently. They play really good football that is nice to watch," he said after the Rangers' Match of Legends game.
"It's intense, defensively and attacking wise, it looks very good. In my opinion, they do deserve to win the league.
"It will still be tough because City will push Arsenal until the last day.
"If you look at this period of time, this is where every single point really counts. There have been a couple of difficult games but they got the three points there, which is what a champion team is made of.
"They have been proving that but the last stretch is always a difficult one. It will be interesting to see but my personal opinion is that they will go for it and they will win the league.
"It has been a while, so I'm happy for them to win it."