
Szoboszlai committed his future to the club this week when he put pen to paper on a new long-term contract. The fresh terms will extend the midfielder's stay at the 20-time English champions until 2031.
By that time it is likely that the legendary Virgil van Dijk will have moved on. The 35-year-old remains the Reds' most important defender but he is now into the final 12 months of his current contract.
With Alisson Becker, Joe Gomez and Wataru Endo also coming to the end of their existing deals next summer, further transition is expected at Liverpool.
But Szoboszlai has been backed as the player to lead it by former Reds and England goalkeeper David James.
Speaking to Grosvenor Sport, James said of the Hungary national team skipper: "He has definitely got the potential to be a future Liverpool captain.
“I mean, the Virgil van Dijk one is interesting because I was trying to do the maths in my head. I think with Ali and Virgil, they are the only two over 30 at the moment, along with Endo.
“But there's part of it where you think, if one of those leaves, does the other one leave? Because then you become the very senior player in a changing room.
“But with regards to Dom, one of my favourite players, of course, many Liverpool fans will have him as their favourite player.
“Iraola has only signed for a couple of years, and I know Pep (Guardiola) only used to sign a two-year deal and he ended up staying at (Manchester) City for 10 years, didn't he?
“So, there's a part of it where you think, if things go well with Liverpool over these next two years, Iraola might stay there longer and therefore someone like Dominik would be that mainstay throughout his tenure at Liverpool.
“We saw some amazing things from Dom last season, and we also saw him playing in a position which wasn't suited to getting the best out of what he was capable of.
“And with Iraola's system, it's high energy, but if he is playing in the right place, then you get the best out of that high energy rather than put him in a right-back position, which didn't necessarily suit that.
“So I think, again, we will see in a fresh environment with hungry players, and time to recover over the summer. We could see some amazing things from Dom.”
The Reds have lost a lot of experience from their dressing room this summer with Mohamed Salah, Andy Robertson and Ibrahima Konate leaving the club on free transfers.
But having signing his new contract, Szoboszlai made clear he is ready to step up his responsibilities. “I want to set the example," he said. “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. This is like a big family and I want to be part of that.”
With Robertson deciding depart at the end of his deal, and subsequently sign for Tottenham Hotspur, it means Iraola will have to appoint a new vice-captain before his side's Premier League opener at Newcastle United on Sunday, August 23.
Szoboszlai and Alisson are expected to be the leading contenders for the role while Gomez and Alexis Mac Allister, who is playing for Argentina in this weekend's World Cup final, could also be options.
And Szoboszlai added: “Is there more responsibility on me now? I think so, yes, even though I am only 25. Mo left, Robbo our vice-captain left, both are club legends, we are going to miss them for sure. Now someone else has to step up and if it's me I'm ready to do it."