The sides will go head-to-head at Celtic Park on September 2 in what will be Gerrard's first Old Firm fixture.
Celtic recorded a convincing 5-0 win in the fixture last season, having already beaten Rangers 2-0 at Ibrox in the early stages of the campaign.
Gerrard's arrival has brought with it a new wave of optimism, however, with four points picked up from their opening two league fixtures and a two-legged aggregate victory over Maribor in the Europa League qualification stages.
The former Liverpool captain penned a long-term deal at Ibrox in the summer with intentions to knock their Glasgow neighbours off the top of Scottish football and build a new structure at the club.
"Of course," Gerrard told BT Sport when questioned whether or not this was the case. "I’ve signed a four-year contract here and everybody realised the size of challenge so we need a bit of patience.
"Celtic is the standard every team in Scotland will try to catch. But I’m really happy with how far we’ve come in a short space of time but for me it’s important to keep trying to build.
"But I’m not obsessed with Celtic – just Rangers. If we keep improving then we believe we will be a challenge for anyone in any competition.
"The thing is, will people be patient enough to give me that chance? I need to earn that chance."
Celtic have won seven consecutive Scottish Premiership titles and went unchallenged for much of last season, ending the 2017-18 campaign nine points ahead of second-placed Aberdeen.
Rangers' final position of third was enough to see Graeme Murty removed as manager and Gerrard appointed on a four-year contract in view of toppling his old manager and current Celtic boss Brendan Rodgers.
The scale of the task is understood by Gerrard, however, who insists he is focused only on his own players for the time being.
"Celtic have set the standard up here over the past couple of years," Gerrard said.
"They’re on the back on two Trebles and we understand how difficult the challenge will be – especially with the first game being away from home.
"But it’s important for me not to be obsessed with Celtic or what’s going on over there. What’s important to me is trying to sort out this house, which is Rangers.
"I need to try to make Rangers better individually and collectively and let’s try to be competitive.
"Celtic have had their own way for too long up here and my job is to try to improve Rangers so that whenever we come up against Celtic or any other challenge that we have a chance to win."
Rangers will host Celtic in the reverse fixture in their final outing of 2018, on December 29.