Iraola has two pre-season games remaining – a double-header against Como on 16 August – before their Premier League season gets under way.
In two weeks time, when they begin their top-flight campaign at Newcastle, the question remains as to who will partner Virgil van Dijk at centre-back.
Alongside Alisson and Cody Gakpo, Van Dijk made his return against Monaco after an extended post-World Cup break.
Van Dijk started the game with 18-year-old Ifeanyi Ndukwe, who looks like a terrific talent but will have to go on loan this season due to work permit issues. It spoke volumes that Liverpool finished the game with Luke Chambers and Wataru Endo at centre-back.
Ronald Araujo, 27, completed his medical on Sunday as his season-long loan move from Barcelona – with an option to buy for around £47.2m – nears completion, while Jeremy Jacquet, 21, is yet to be involved in full training since completing his move from Rennes.
Jacquet suffered a shoulder injury in February and has recently struggled with a minor knee problem, but Liverpool are optimistic he could play next weekend against Como.
“Jeremy Jacquet, we were in doubt whether to put him in,” said Iraola. “We decided not to, but he should be fine for the next one. It’s taking a bit more time than we were expecting.”