The midfielder scored one goal and provided two assists in 34 league appearances last season, 18 of them starts, and is under contract until the summer of 2027.
Jones has been strongly linked with a move to Inter Milan throughout the season, with the Italian club having publicly confirmed their interest.
La Gazzetta dello Sport reported this week that Inter have made a concrete attempt to sign him, with a bid of €20m lodged for his signature.
Liverpool, however, are believed to want €30m to part with the midfielder.
Transfer journalist Nicolo Schira now reports that the two clubs are expected to hold discussions over a potential transfer next week, in an effort to reach an agreement.
According to Schira, Jones is Inter's priority target for a new midfielder, and the Italian club have already agreed personal terms with the player on a contract running until the summer of 2031.
The gap between the two clubs' valuations — a difference of €10m — leaves the deal unresolved for now, but with personal terms already settled and Inter treating Jones as their leading target, the coming week's talks are likely to prove decisive in determining whether the midfielder leaves the only club he has ever known.
A move would mark the end of Jones's time at the club where he progressed through the academy and made his first-team debut in 2019, having grown into a regular contributor to Liverpool's midfield in the years since under three different head coaches.
For Inter Milan, signing a player of Jones's profile would add Premier League experience and ball-progression qualities to a squad already chasing several midfield targets this summer, with the Italian club determined to refresh a unit that fell short of expectations domestically last season despite their continental ambitions.