The 26-year-old played 35 games for the Reds last season after completing a £7m switch from Newcastle United to Anfield last summer.
Enrique, whose future at Liverpool has been cast in doubt of late following reports Brendan Rodgers wanted to sell the Spaniard, is focusing on improving and helping the club win silverware on a regular basis.
“I want to play here for as many years as I can and play as many games – I hope to be like Carragher but that would be really difficult,” he told the club’s website.
“I want to stay here because it’s an amazing club and a big club and every player dreams of being here. I also want to win as many titles as I can. I’ve played in English football for five years and it’s amazing to play here.
“But I’m still learning. At teams like Liverpool you learn quickly; in one year here I have learned a lot and with this manager I have learned plenty too.
“The manager gives us simple instructions. He says more things during the week than he does in his pre-match team talks.
“He has tried to instruct and improve every player and I think this is a good thing because everyone is still learning. I still make mistakes, so I have to learn.
“The manager wants me to make more assists and score more goals and play more like a forward. He has told Glen Johnson and Martin Kelly to do the same and Stewart Downing in the left-back role. He wants us all to play like wing-backs. I really like to play like this.”
Enrique also backed Rodgers decision to utilise Stewart Downing in a left-back role this season, providing competition for the Spain international and youngster Jack Robinson.
“It’s a good thing because before [Downing played left-back] there was just myself and Jack Robinson,” he added.
“With the way we intend to play, that is with the right-back and left-back attacking, Stewart can fit in well.
“He’s a good lad and I’m happy for him. We have many, many games this year and so it’s good to have competition for places.”
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