Jones has moved into the final year of his contract at Liverpool and the Premier League side want to cash in on him now to avoid losing the England international for free in 2027.
The 25-year-old has featured for Liverpool in their USA preseason tour as negotiations with Inter continue after they failed to sign him in the January window.
A move to the San Siro appeals to Jones, who is unlikely to be a starter under Andoni Iraola, and the two clubs are close to a fee compromise between £30M and £35M.
Romero is also expected to cost around the same amount with Tottenham boss Roberto De Zerbi confirming he's spoken to the Argentina star about an exit to Milan.
The two transfers, plus a sizeable salary package for Romero, could cost Inter in the region of £100M - which they will need to raise via player sales.
Reports in Italy claim Benjamin Pavard, Kristjan Asllani and Davide Frattesi have been deemed as available for sale, but Inter cannot move forward on Jones or Romero, until they start to make offloads.