In a BBC Sport interview with Liverpool CEO Billy Hogan in New York, the message was clear: FSG will keep investing to do what’s needed to put the team in position to win.
With Szoboszlai, Ryan Gravenberch and Alexis Mac Allister, Liverpool look well stocked in midfield.
Szoboszlai and Gravenberch signed new contracts this year, while Iraola will aim to get the best from Mac Allister after an underwhelming season.
Curtis Jones’ move to Inter Milan appears to be nearing completion, with Liverpool open to a sale around £35m.
Any deal could also hinge on the future of 19-year-old Trey Nyoni, who impressed in pre-season. There’s positive news with Wataru Endo and Stefan Bajcetic back in training, while Harvey Elliott’s next steps are still to be determined.
Liverpool made an enquiry about Adam Wharton earlier this year, but they are not alone in pursuing the Crystal Palace midfielder.
At least one more addition is expected up front, with PSG’s Bradley Barcola now Liverpool’s primary target after missing out on Yan Diomande. Liverpool have already brought in Victor Munoz from Osasuna for £34m.
It’s not quite right to call Barcola a straight Mohamed Salah replacement, but with PSG valuing him at £145m, his signing would be a major statement.
Liverpool would prefer a fee closer to £100m, and Barcola is open to an Anfield move, though there are currently no talks between the clubs.
With Salah’s departure, expect more minutes for 17-year-old Rio Ngumoha on the right flank.
Ngumoha looked more comfortable on his favoured left against Leeds, but he has the tools to be effective on either side for a manager who wants interchangeable wingers.
Alexander Isak and Florian Wirtz started pre-season encouragingly, but a decision is needed on Federico Chiesa, who wants to fight for his place at Liverpool despite links to a move back to Italy.
Kieran Morrison, 19, enjoyed a strong tour, scoring the first goal of the Iraola era, and will likely head out on loan depending on depth. More youngsters are set for loans in the coming weeks.
In June, BBC Sport revealed that Tottenham were among the clubs monitoring Cody Gakpo, but any move would only happen if Liverpool have a replacement lined up, and with four years left on his deal, the Netherlands international would be expensive.
Liverpool still see him as a proven, versatile Premier League attacker, and with Hugo Ekitike unlikely to feature this year due to a ruptured Achilles, letting Gakpo go would be a significant call.
Mike Gordon, FSG’s president and effectively Liverpool’s managing owner, was in Chicago on Sunday.
Like many connected to the club, he will have seen the first-half excitement for the Iraola era, followed by the second-half reminder that this squad still needs further additions.