The Reds made an inauspicious start to life under the former Borussia Dortmund manager when he took over from Brendan Rodgers in October, but since early February they have lost just once in their last 10 league matches, as well as reaching the Capital One Cup final and the Europa League semi-finals.
They are now looking to secure European qualification for next season, either for the Europa League through their league finish or for the Champions League by going all the way in this year's Europa League.
Gomez is yet to play under Klopp after being signed last summer by Rodgers, as his promising start to his debut campaign at Anfield was cut short by a season-ending injury at the start of October.
However, the teenager believes that the club should be targeting winning a first league title since 1990 from the get-go next season under the German boss.
The 18-year-old told the Mirror: "Being at Liverpool, every year your main aim is to win the title and to compete for that. Next year’s a new campaign and from day one that’s what everyone’s aims will be. I don’t think anybody expects any less - especially the manager.
"Leicester have been surprising. But it’s the Premier League, anything can happen. From this year, it just goes to show that you can’t tell. At the start of the season, you’d have been surprised if someone would have told you that Leicester and Tottenham would be the two teams competing for the title.
"What it goes to show is that with a good team spirit, a good team will go and compete. The main thing for us is to stick together as a team. If we do that, I don’t think anyone could beat us because we have so much talent."
Liverpool face Villarreal at El Madrigal in the first leg of their Europa League semi-final this evening ahead of a trip to Swansea City on Sunday.