Jones was a key squad player for the Reds during a difficult campaign and featured in 34 of their 38 Premier League matches, predominantly as a central midfielder but also on the right side of defence.
However, with the 25-year-old entering the final year of his contract at Anfield, Liverpool can either offer him fresh terms or sell him this summer to avoid losing him on a free transfer.
Inter Milan have already shown an interest in Jones, as revealed by the club's sporting director Piero Ausilio, and they could submit a bid for the midfielder.
According to The Athletic, the versatile player is valued at around £35 million, but the sticking point is whether Inter are willing to match that asking price.
Jones has already asked teammate Federico Chiesa what it's like to live in Italy following links to the Milan giants, and it seems likely that he will depart unless Iraola wants to keep him.