Liverpool are keen on handing a new deal to Suso, according to the midfielder's agent, who also confirmed that a move to AC Milan in future is a possibility.
The 20-year-old's contract at Anfield runs out at the end of this season and the Reds have not offered an extension. The Spaniard spent the last season on loan at Almeria and impressed during his time with the La Liga outfit.
Suso returned to Liverpool earlier in the summer and has made two appearances in all competitions for Brendan Rodgers' side this season. The midfielder picked up a groin injury in October and is likely to return to action next month.
"There is no agreement with Milan. It is certainly a possibility, but for now, there's nothing more to say," agent Jaume Serra told Calciomercato.it.
"Rather, Liverpool are pushing for his renewal, so we cannot rule even this hypothesis out. At the moment, it's too early to discuss any possibilities."
When asked if Napoli have made any contact in signing Suso, the player's representative said: "No, I've never had any contact with Napoli. For now, we can rule out this possibility. There's no interest from them."
AC Milan CEO Adriano Galliani had earlier discussed the possibility of bringing Suso to San Siro. The Italian giants have long been monitoring the playmaker and could sign him on a free transfer if Liverpool fail to tie him down to a new deal.
"Transfer market? I know where we can improve, but I don't tell that to you. Suso? He has an expiring contract and he'll tell us if he wants to move or stay," the Milan chief executive told Gianluca Di Marzio.
Earlier in September, Suso had asked Rodgers for more playing time. It should be seen whether the midfielder will be involved in the former Swansea boss' plans at Anfield once he returns from injury.
"I haven't played in a long time. Being on the pitch after a long time, I was really happy. And after the goal, I was over the moon," Suso told Liverpool's official website.
"It's the manager who decides. I am going to be there. If he wants to use me again, I will be there."