The 20-year-old Spaniard spent last term in his homeland, making 33 appearances as the La Liga side avoided relegation.
|5/6||Liverpool are 5/6 with William Hill to finish in the top four|
"After the season in Spain, I think I have become a better player - I learned a lot," the playmaker told Liverpool'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."
Suso made his breakthrough at Liverpool as a teenager in 2012-13, as he made 14 top-flight appearances in Brendan Rodgers' first season in charge.
And the Spain Under-21 international says that he has held positive talks with Rodgers about his prospects with the Premier League runners-up.
"I came here in December at Christmas when I had my week of holidays....I came here for two or three days to have a meeting with the manager," Suso added.
"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 - for me, there is no bigger club than Liverpool."