The Serie A champions had a loan bid for the England international rejected at the start of 2026 as former Reds boss Arne Slot wanted to keep him for the second half of the 2025/26 season.
However, his starting place in Andoni Iraola’s plans looks unclear, and Inter have continued to monitor the 25-year-old ahead of the 2026/27 season.
Inter initially reached out with a June offer in the region of €25M (£21.7M) - but that was rejected by Liverpool, who value him closer to £35M (€40M).
Jones is now into the final year of his contract at Anfield, and despite being unlikely to sign a renewal on Merseyside, the club are still unmoved over their transfer demand.
According to reports from Italian outlet Calciomercato, Inter have contacted Liverpool again over a move, after taking a few weeks to reassess their position.
They are unlikely to offer move than put forward in June, but Jones' willingness to leave could tip the balance, and persuade Liverpool to accept a compromise.