Jones is now into the final year of his contract at Liverpool and the Premier League side want to sell him this month to avoid losing the England international for free in 2027.
The 25-year-old featured for Liverpool in their USA preseason tour, as negotiations with Inter continue after they failed to sign him in the January window, and he was omitted from the squad to face AS Monaco today.
The main stumbling block has been over an agreed fee, with the two clubs now arriving at a compromise package of between £30M and £35M, as he prepares to move on.
Inter are balancing their finances delicate to bring in funds via some San Siro sales, but they have not managed any sales so far, despite shifting Yann Sommer, Francesco Acerbi, Matteo Darmian and Stefan de Vrij off their wage bill as free agent.
However, the club could now fast track Aleksandar Stankovic's €40M+ move to Brentford, after rejecting the Bees first offer on the Serbian.
Stankovic was sold to Club Brugge last summer, but Inter activated their €23M buy-back clause on him, with the plan to sell him on again for bigger profit.