Jones is entering the final year of his contract, meaning Liverpool could cash in now rather than risk losing him for free in 2027 if he does not sign an extension which is looking increasingly likely.
The 25-year-old's long-term future remains unresolved heading into the new season and his frustrations have already shown in preseason as he was seen in dispute with his teammates following the win over Wrexham.
Reports and footage showed the pair exchanging words for around two minutes after the final whistle as the two of them argued over the captain’s armband.
Inter Milan tried and failed to sign Jones over the winter and TeamTalk now report that a "breakthrough" has been made in an attempt to land the Liverpool born midfielder who is keen on the switch.
Jones has racked up 228 appearances since his Liverpool debut in January 2019 but is seeking more regular first-team opportunities which Inter can offer him under manager Cristian Chivu.
Earlier this month Liverpool manager Andoni Iraola stressed he wanted Jones to stay at the club, even if he cannot offer him solid game time.
"I rate Curtis very highly," he said. "For me he is a great, great player, and I hope he can continue with us and continue performing the way he has been performing."
Liverpool have placed a £35m valuation on Jones but Inter are reportedly aiming to snag the academy star for around £30M as talks continue this week.