Reds boss Brendan Rodgers is likely to reshape his squad this summer, but Enrique is hopeful he is part of the manager's plans.
The 27-year-old left-back is under contract until 2016 and believes he is developing well at the club.
"I haven't spoken with the manager about next season but I want to stay," Enrique said.
"I still have to improve some things but I think I'm getting better every season. As you get older you know more.
"This type of football the manager wants has really helped me as it's the type of football I love to play.
"I am happy at this incredible club and in this city. The support we get from the fans is amazing and also from people inside the club who do so much for us.
"I still have three years on my contract and hopefully I can stay at this club for many years."