The Reds captain has just 18 months remaining on his current deal with the Merseyside club and hopes that manager Brendan Rodgers will offer him the chance to extend itLiverpool captain Steven Gerrard has pleaded with manager Brendan Rodgers to renew his current contract, which is due to expire in 18 months' time.
The Reds midfielder made just 18 Premier League appearances last term, as a number of niggling injuries kept him out of Kenny Dalglish's team.
However, after starting all six of the Merseyside club's league games so far this season, the 32-year-old insists that he is as fit as ever and wants to continue his career for as long as possible.
"I am contracted for another 18 months or so," he told Sky Sports News. "I am really happy. I am enjoying my football. I feel physically strong.
"I want to go on for as long as I can. I love playing for the club. I am captain. I am living the dream. I do not want that to end.
"Hopefully I can play and contribute in this new regime under Brendan Rodgers, because it is very exciting."
Liverpool face Udinese in the Europa League on Thursday and the Reds star hopes that his side can build on the momentum created by their 5-2 win over Norwich City on Saturday.
“It gives you huge confidence and belief when moving into the next games," he continued.
"But we knew, as players, if we kept listening to the manager and listening to the messages he was putting across, the first win was only round the corner.
"It should have come against Manchester United the week before. It should have come against Manchester City three or four weeks ago.
"If we keep playing the way we are playing and keep showing the same effort and determination, there will be many more wins just around the corner."