The midfielder, who came close to joining Chelsea seven years ago, has remained loyal to his hometown club though several periods of transition.
An eighth-placed finish last season suggests the Reds are no closer to challenging at the top, and Sven-Goran Eriksson said this week Gerrard must leave if he wants a winners' medal.
Liverpool have begun another rebuilding process under Brendan Rodgers, but the captain told Sky Sports News: "I don't think we're miles away.
"We have to be realistic and we finished eighth in the league last year, but we got to two major cup finals which shows that we are a good team and we can compete with anyone on our day.
"If we find a better level of consistency at the club, I think we can find ourselves higher up the table than last year.
"Who knows what's around the corner? For me, I just take each game as it comes and hopefully before I hang my boots up I can realise the dream of winning it, but I'm also realistic as well."