According to The Athletic, Inter submitted an offer worth around €25 million (£21.7m; $28.7m), which was immediately turned down by the Reds.
It marks the Italian side’s second attempt to sign the 25-year-old this summer, but the proposal remains well below Liverpool’s valuation.
Jones, who has entered the final 12 months of his contract, is valued by the Reds at around £35 million, with club officials insisting there is no realistic pathway to a deal unless Inter significantly improve their offer.
Liverpool are even prepared to risk losing him on a free transfer next year rather than accept a reduced fee.
The club are using recent Premier League deals as benchmarks to justify their stance, while Inter are now reportedly seeking new ways to raise funds to revive their interest.