Inter Milan were interested in his availability in January, and earlier this month Pierre Ausilio, Inter's sporting director, said: "Curtis Jones - we are paying attention to him. We didn't hide. We understand what the developments will be."
Federico Chiesa went as far as telling La Gazetta that Jones asked him what it is like to live in Italy. Chiesa told him the weather was certainly better in Milan than it is in Liverpool.
The prospect is there, with Jones knowing that he would be a key part of an Inter side that sees him as one of their main priorities for the summer.
For Jones, whose close friend Anthony Gordon moved to Barcelona, perhaps the glamour of Milan is appealing.
Yet there is certainly a different dimension to this debate, given Jones' background and his own ambitions. His frank nature and willingness to take responsibility, as well as his versatility, are all attributes praised widely by those at Liverpool.
Jones stepped up to take the third penalty against PSG in the Champions League in 2025 and after his spot-kick was saved by Gianluigi Donnarumma, he said it was all a part of his journey.
"I can live with missing, but I can't live without taking responsibility. I see myself as being a lad who wants to take risks. I want to be a lad who's relied on by the team, the staff, the fans, and I want to be a huge star," Jones told GQ in 2025.
From a Liverpool perspective, they must also assess the value that Jones brings to the dressing room when it comes to understanding the club and the fanbase.
With a number of senior figures leaving this summer and the likes of Alisson Becker, Virgil van Dijk and Joe Gomez all on contracts that run out next summer, perhaps it would make sense for Iraola to see if there is a future with Jones when pre-season starts next month, before both parties can decide on next steps.
There is no doubt that Jones is a terrific asset to have in a squad and it's worth noting that he actually played more games last season than in any other campaign for Liverpool. But 21 of those 49 appearances came off the bench and he only started 10 Premier League games in midfield.
The question too is whether he would still be content with such a role?
"I want to be humble and not say things like I'm going to be captain and things like that but I want to be captain of the team," he told Sky Sports in December.
"I want to stay here all my life like the man I look up to in every way. That's Steven Gerrard and everybody knows that. If I could follow him, that would be great. I would never complain and I'd always have a smile on my face."
That much is enough to know about Jones' long-term ambitions but in the here and now, Liverpool know that it is imperative for a decision to be made this summer.
