Record signing Alexander Isak also returned to Liverpool training this week.
He, Florian Wirtz and Ryan Gravenberch all missed the trip to New York, where Liverpool beat Wrexham 1-0 in their second pre-season fixture, but are expected to feature on Sunday against Leeds.
Jeremy Jacquet missed training but was in the gym as the club carefully manage his recovery from the shoulder injury he sustained in February.
The centre-back is a doubt for the weekend, despite Iraola suggesting earlier in the week that he would feature.
Joe Gomez, who has been ruled out for the start of the Premier League season, was also in the gym.
Once the warm-ups were done, the intensity in Iraola’s drills was clear to see. He likes to get heavily involved and was particularly animated, using phrases like “play in possession” and “quicker, quicker” repeatedly.
There were celebrations between players whenever they scored in the mini-drills and the atmosphere was generally positive, with Iraola unafraid to step in and point out something, or discuss a player’s position.
The squad then separated, with one group moving on to a smaller pitch for a nine-a-side match while another group worked on set-pieces with Iraola’s assistants, Tommy Elphick and Shaun Cooper.
Wirtz was on corner duty, while Elphick even put on a bib to get involved.
Watching on was Mike Gordon, the Fenway Sports Group president, who is now overseeing Liverpool operations again. He is expected to be at the game on Sunday at Soldier Field in Chicago.
Liverpool had a team dinner on Thursday evening, with Iraola sharing a beer with the likes of Phil Thompson and Robbie Fowler after.
Thompson told BBC Sport they spoke about a number of things, from the season ahead to their families.
Iraola was not even born when former defender Thompson won the third of his three European Cups for Liverpool. But this was a sign of the new head coach recognising the legends of the club and the weight they still carry.
Iraola still has three weeks before his first Premier League game as Liverpool manager – but the seeds of his tenure are getting planted here in the Windy City.
