Negotiations with Liverpool are far from straightforward, particularly because of the financial distance between the two parties, but the Serie A club have not abandoned the pursuit of the midfielder as the transfer window continues.
That was indirectly confirmed by Inter sporting director Piero Ausilio, who has suggested in recent days that the file on Jones remains open at the San Siro despite the financial gap between the clubs.
Liverpool continue to value the 2001-born midfielder at just over €40 million, a figure which Inter Milan still consider to be too high for their current budget and transfer plans this summer.
The hope in Milan is that as the weeks pass and Jones' contract situation edges closer to its expiry date, Liverpool may be encouraged to lower their asking price for the England international, who has continued to be strongly linked with the move throughout the window.
Nottingham Forest have also entered the race for Jones in recent days, though according to Corriere dello Sport, their interest may have strengthened rather than complicated Inter's own plans for a deal this summer.
Jones is understood to have reiterated to Liverpool his own preference for a move to Inter, confirming his liking for a switch to Italian football over other suitors.
The report describes it as an important signal from the player, even if not yet sufficient on its own to unlock the negotiation between the two clubs.
Inter continue to view Jones as an ideal profile to add quality and dynamism to their midfield options for next season.
That appreciation is also said to stem from a specific recommendation by head coach Cristian Chivu, who was left particularly impressed by the midfielder's performance in the Champions League meeting between the two sides last December.