Gerrard insists he is not thinking about his long-term future just yet but believes he can play on beyond his current contract.
The 32-year-old signed a new deal in January which runs until the end of next season but he does not necessarily see that as a natural finishing point.
"We will have to wait and see," said the midfielder at a golf event for his charity The Steven Gerrard Foundation.
"I'm enjoying my football, I feel physically strong, and I want to go on for a long time yet.
"I love playing for the club, I love being the captain. It's living the dream, so to speak.
"I'm enjoying playing under Brendan Rodgers. The training is good, it's a very exciting time, and hopefully I can continue to play and to contribute under the new regime."