Spurs enjoyed an excellent end to last term and pipped rivals Arsenal to a top four finish to secure qualification for this season's Champions League.
So far this summer, manager Antonio Conte has wasted little time in strengthening his squad with no less than six new faces introduced to the club.
They include Fraser Forster, Ivan Perisic, Yves Bissouma, Clement Lenglet, Richarlison and Djed Spence.
With more potential signings on the way, fans have every reason to be optimistic ahead of the upcoming campaign and O'Hara is aiming high.
Asked by talkSPORT co-host Jason Cundy about the potential of a top four finish, O'Hara told The Sports Bar: "I don't think that's a great season.
"If we finish fourth next season that's not progress with the players that we've signed."
Discussing their chance of catching Liverpool, O'Hara added: "I'm optimistic. Genuinely, I'm optimistic.
"I wouldn't put my house on it, but I look at the squad of players that we've signed and if we finish fourth then I'm not going to be happy.
"I'm not going to be happy with a fourth place finish and no trophy."
Liverpool have added the firepower of Darwin Nunez and Man City have signed Erling Haaland in a bid to pull further away from the pack.
Spurs play City away on 10 September and host Liverpool on 5 November.