Szoboszlai scored and was hailed by Liverpool teammate Mohamed Salah after their FA Cup win against Brighton on Saturday.
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Salah declared the Hungary midfielder among "the best players in the world right now".
Szoboszlai is also being tipped - like Gerrard - as a future Liverpool captain, but he is keen to duck any type of comparison.
He said, "I won't play Gerrard's season; he was a legend for the club.
"I'm just trying to write my own story and give my all in every game. I hope to make it to the end."