The 23-year-old arrived in the summer in a £60m deal from RB Leipzig, as Liverpool moved to strengthen in midfield following the departures of Fabinho, Jordan Henderson and Alex Oxlade-Chamberlain.
It has been a strong start to life in England from Szoboszlai, who scored his first Premier League goal earlier this season against Aston Villa and provided two assists in his side's recent win over Nottingham Forest.
Szoboszlai has previously stated Liverpool's target must be to win "everything" this season, believing they have the depth to compete on all fronts domestically and in Europe, and the Hungarian star has suggested everyone in the squad has a hunger to play, something that was perhaps previously not always the case at Anfield.
"Everyone wants to get into the starting XI, that’s normal and that’s how it should be, the goal in every team," he told journalist Ben Bocsak.
"Who is satisfied with sitting on the bench? I’m going to be honest, there are a few. Actually before I came here there were some [at Liverpool] as well."
"I won’t name names, but I heard about it."
Szoboszlai is the only outfield player to not miss a minute for Liverpool in the Premier League so far this season, featuring for the full 90 minutes in all 10 matches, and he started in the fourth-round Carabao Cup win over Bournemouth too.
That workload is something that Szoboszlai wants, as he urged Jurgen Klopp to keep playing him regardless of the competition or opposition.
"Personally, I want to play in every game, even if I’m a bit tired," he continued.
"Anything, whether it’s the FA Cup, League Cup, Europa League, Premier League, national team, anything."