The 20-year-old spent last season on loan at Almeria as Liverpool challenged for the Premier League title, and it would seem as though the youngster's chances of appearing for the Reds have extinguished with the arrival of fellow attacking-midfielder Adam Lallana, while Lazar Markovic is also expected to finalise a move to the Reds in the coming days.
However, the Spaniard believes that he has improved following a season on loan with Almeria, for whom he made 33 appearances last season, and he has said that he wants to challenge for a place in Brendan Rodgers's starting XI.
"After the season in Spain, I think I have become a better player - I learned a lot," Suso told the club's official website. "Obviously Liverpool are going to sign a lot of players because we are in the Champions League this season, and we have to have a good squad because there are a lot of competitions.
"But if I fight for my place, I do my best every day in training and when I have the chance to come on or start a game, if I do well, I could have chances to play a lot of minutes in the first team.
"I came here for two or three days at Christmas when I had my week of holidays to have a meeting with the manager. He talked to me, said he was happy with what I was doing and said that this season he wants me to stay here. I want to stay here and sign a new deal."
Suso has made just 14 appearances for the Reds and is yet to register a goal for the club.