On Thursday, the 31-year-old agreed a new deal which will keep him at the club until the end of his career - but the midfielder has not set a date on when that will be.
"I'm hoping to play beyond the length of this contract," he told the Liverpool Echo. "I'm feeling fit and strong and I want to play for as long as I can.
"I don't want to put any time frame on it. As long as I feel good and I'm performing at the top level I'll keep going.
"Hopefully over the next few years I'll earn another contract with my performances.
"But even if Liverpool don't offer me another contract after this one I don't think I could play for anyone else. I've been at this club since I was eight and I'm living the dream."
Manager Kenny Dalglish said Gerrard's example of staying at the same club for his entire career was a rarity.
"It doesn't happen very often but it depends on the people and if they are happy where they are and happy with the people they are working for then why would you move?" said the Scot.
"Everyone knows the service he has given to the club and the success he has brought to the club and knows how much it means to him.
"For him to be extending his contract and looking to work here beyond playing is a great lift for everyone here."
Gerrard will take up an ambassadorial role for the club when his playing days are over.
And Dalglish said they were also looking at doing the same with Jamie Carragher, 34 later this month, who also came through the academy.
"We will have the same conversation with Carra to try to keep him at the club as long as we can and involved with the club," he added.
"We will see what his plans and ambitions are and what he would like to do.
"It is hugely important for the club to keep people who have been as great a servant as those two have in and around the club in some shape or form.
"If they want to be here then we should do what we can to accommodate them.
"They are fantastic assets to the club on and off the pitch and it is something we should look to develop."