The Hungary international is currently in talks with Liverpool after extending his deal, which currently runs to 2028.
Szoboszlai struck in last night's Champions League win against Galatasaray, with a watching Gerrard hoping the midfielder stays and eventually becomes club captain.
Speaking on TNT Sports, Liverpool icon Gerrard said: "I hope he stays longer. I think there's a future captain in there for Liverpool."
Speaking to Szoboszlai in the aftermath, Gerrard continued: "Can we just talk through the goal? It's looked as if obviously it had been planned on the training pitch? (Alexis) Mac Allister obviously pulled it back. Was it meant to be for your right leg? How quick did you have to change your mind and adjust?"
Szoboszlai replied: "To be honest, it was true. I just see my direction and how I go to the ball, it was striaght and then I have to react because it was really close to the backline of the defender. But yes, it looks like I don't just have a right foot."