The Premier League is the only club honour the 33-year-old midfielder has yet to win, but with the Reds top of the table with just six matches to go, anticipation is growing at Anfield.
Manager Brendan Rodgers and the players continually insist they are taking things one game at a time, but even the vastly-experienced Gerrard is struggling to keep the fans' infectious optimism at bay.
"I think I'd be a liar if I said no," said Gerrard, when he was asked whether he was dreaming about winning the title.
"It is flashing in and out of my mind from time to time, but I am trying to get it out as quick as it is going in because nothing has been achieved yet.
"It is important for myself and the players to try to not forget about the dream but try to park it up, as dreams only happen when you get the job done and there are six hard matches still to play."
Four goals in five matches in March saw Gerrard win the supporters' player of the month award, but he admits there was some fierce competition.
Striker Luis Suarez scored six - including a hat-trick at Cardiff to take his season's tally to 29 - while midfielder Jordan Henderson put in a number of stand-out displays and young winger Raheem Sterling has come to the fore.
"For the first time in a long time it could have been any one of the starting XI of late. This is more of a team award," Gerrard told LFC TV.
"I am really happy (with the award). I am very critical person after every performance and every training session, but I'm very pleased how I'm playing and contributing well to the team and doing a job the manger is happy with.
"That is why I come to work really, to perform well. If I am playing well and the manager is happy with me you'll see a happy Steven Gerrard."
Gerrard has, for so long, led the way on and off the pitch for Liverpool, and despite having a world-class player like Suarez in the side, he still feels a responsibility to set the standards.
"I have a vital role every single day, that is the captain's job in the team, but nothing changes," he added.
"I come in and work as hard as I can and I try to lead by example for all the younger players watching me train every day, and hopefully they follow suit on the pitch.
"That is what has been happening. The experienced lads have been setting an unbelievable example and I think that has really helped, because growing up as young lad I used to look to the older players to see what they had done and I wanted to copy them.
"Myself and the experienced lads have such an important role, but for everyone we keep doing what we are doing.
"I've noticed of late players in interviews saying how healthy the squad is, and it is the players pushing for places who are keeping the starting lads on their toes."
The visit of title rivals Manchester City and Chelsea to Anfield this month are being billed as decisive games, but Gerrard stressed every opponent has to be treated equally - starting with the next one, which happens to be West Ham on Sunday.
"Nothing changes, we don't worry about Manchester City, Chelsea, (Crystal) Palace, Norwich or Newcastle - we worry about beating West Ham (on Sunday)," he said.
"We approach it how we've approached the last eight games (all victories).
"We have an unbelievable mentality, winning attitude, and we always know if we work hard for each other and do the ugly bits which players don't like doing all the time, we know the nice stuff will come out.
"We have been playing at a pace which is difficult for opposition teams to cope with, but it all starts with sticking together.
"It is the manager's way. Everyone has taken it on board and put it into practice.
"I remember us finishing the last six months of last season very consistently and we took that into this year. We had a good pre-season and from day one the form has been consistent, but of late we've taken it to another level.
"The run we are on is superb and it is a credit to everyone in the squad."