The Gunners last won the title in 2004, when Arsene Wenger’s side went unbeaten throughout the league season.
Mikel Arteta’s side pushed Manchester City close last season but eventually missed out by five points.
The Gunners are back in contention this term, and trail leaders Liverpool by two points.
And Cech, who spent four years at Arsenal after leaving Chelsea, believes the Gunners will come out on top in May.
Asked firstly which of his former clubs will win a title first, Cech said on Monday Night Football: ‘At this moment I think Arsenal.’
‘This season? I think this season it will be very close but I actually think Arsenal might do it.’
City have won five of the last six championships and are the favourites to do so again.
Pep Guardiola’s men are also two points behind Liverpool but they have a game in hand.
Arsenal visit Burnley on Saturday before renewing their Champions League campaign against Porto in Portugal.
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