The 25-year-old, who joined from RB Leipzig for £60m in 2023, was the standout performer for the Reds last season, scoring 13 goals and providing 12 assists as speculation swirled around his future.
Szoboszlai had two years left on his previous deal, but talks accelerated in recent weeks before an agreement was reached and signed this week, ending any uncertainty over his long-term future. Both club and player believe his best years are still ahead of him.
"There's always more to come. I'm never happy," Szoboszlai said. "I want to set the example. I want to be an example also for everyone, as much as I can.
"When I signed, I said I want to win everything. That didn't change for a little moment either. It stayed the same. I want to win everything that is possible in this country, also let's say the Champions League. I'm ready to go for it."
The Hungary international also spoke about his excitement at working under new head coach Andoni Iraola, who joined Liverpool this summer.
"I think he showed it in Bournemouth that he is an unbelievable coach. Always competed with us with the most fit team in the Premier League. With the intensity how he wants to play and the knowledge that he has, I think he's an unbelievable coach. I'm looking forward to playing under him," Szoboszlai said.
Reflecting on the mood in the squad as pre-season training got underway, Szoboszlai described a positive atmosphere around the club following a difficult campaign last term.
"You come back from the summer holiday, you didn't see the guys for two months, and the old guys who came back from loan: Kostas and Harvey. So, happy to see them. Everybody is trying to be positive as much as possible, which right now is easy, but we have to keep on going, keep on working hard. This is what we need, I think," he said.
Asked how much motivation last season's disappointment provides for the campaign ahead, he added:
"It shouldn't be a pressure, it should be a motivation that you don't want to do the same thing, the same mistakes we have done last season. That's the motivation we have to take. Everybody has to take responsibility, probably the older ones even more, then the younger ones can follow the older ones. We have to become again a team."