Brendan Rodgers' men travel to Carrow Road on Sunday knowing that an 11th consecutive Premier League victory will bring them a step closer to a first league title in 24 years.
"Every game is getting bigger because we are getting closer to the last game of the season," he told reporters.
"Manchester City was always going to be huge because they are in the race with us but Norwich now become Manchester City. Norwich become Chelsea. Norwich become Manchester United. That's how big it is.
"We have got to treat Norwich like we treated AC Milan in 2005. That's just how football is. We can't think about what color shirts Norwich are wearing and the personnel in them.
"We have got to treat them like the best team in the world."
Liverpool's winning streak - which includes triumphs over both Manchester clubs - has earned it praise from all quarters, but Gerrard warns his team has won nothing yet.
"It is a remarkable run but you get nothing for it," he added. "You get a pat on the back. We've all had them but they come and go. What is key as a footballer is getting something to show for all the hard work.
"We have been on a magnificent run. We could win 13 on the spin but lose the last one and we will get nothing. Nobody will remember it. The only way people will remember it is if we go on and win it.
"We have got to forget where we are and forget what we have done. We have just got to focus and prepare for Norwich now. We have got to treat it like it is the last game of all our careers. That is the mentality."