Szoboszlais star is undoubtedly on the rise following his switch to Anfield, not least due to the speed in which he has settled.
The 22-year-old was at least a contender for Man of the Match in each of the last three games for the Reds, scoring his first goal for the club in the 3-0 win over Aston Villa.
Thursdays 2-1 victory over Serbia served as Szoboszlais first appearance for his country as a Liverpool player, playing the full 90 minutes as captain.
Speaking to journalists including Indexs Andras Gall after that game, the midfielder rejected suggestions he should be viewed as a superstar.
Even as a Liverpool player, I am the same Dominik Szoboszlai as I was, he insisted.
Here, everyone is equal in the team, everyone looks at each other the same way.
I want to set an example and help the team. I would like to avoid being seen as a superstar.
Of course the media writes what they want, but I dont want this to be a topic within the team.
There is a humility in the Hungarian that makes him a perfect fit within Jurgen Klopps squad, and though he looks set to emerge as one of the most important players at the club, that will not change his attitude.
That is exemplified in how hard Szoboszlai works both on and off the ball, with the former RB Leipzig midfielder twice required to play as one of two No. 6s already following red cards to team-mates.
It is this quality that those inside Anfield may grow to cherish the most, regardless of the goals and assists he inevitably provides.
Just as with Hungary, Szoboszlais focus on the team, rather than the individual, will only make him even more of a favourite on the Kop.