The Anfield club finished seventh last season, 12 points behind Arsenal in fourth but a mighty 28 adrift of champions United.
But the Reds have won both their league games this season as well as edging out Notts County in the Capital One cup earlier this week, and Gerrard feels they are getting closer to challenging at the top of the table.
He told the Liverpool Echo: "For a long time, the gap between ourselves and United, Chelsea and now Manchester City has been too big.
"Each year we have been trying to close that gap, so really this season isn't any different in that respect.
"But it does feel slightly different this year. The team spirit is really good and there is a belief within the squad."
United will travel to Anfield on the back of a 0-0 draw with Chelsea at Old Trafford last time out to follow up their resounding victory at Swansea on the opening day of the season.
Tottenham's season and pre-season have been overshadowed by the saga of Gareth Bale's move to Real Madrid which is apparently imminent.
Spurs have managed fine without the Wales international, winning their two games so far, and former England and Tottenham defender Ledley King is sure the club will be able to survive without their leading talisman so long as the players Bale leaves behind step up and take responsibility - starting in the north London derby against Arsenal on Sunday.
"You need everyone pulling in the right direction," said King, who is now a club ambassador.
"We do have players in the squad who can score goals throughout the team so rather than relying on one person this season it's going to be much more of a team effort and they need to put in hard work to get the results."
It has been a turbulent start for Arsenal whose fans expressed their frustration after the opening-day home defeat by Aston Villa which was followed by victory at Fulham and progression to the Champions League group stages.
On Thursday manager Arsene Wenger revealed forward Lukas Podolski could be out of action for up to 10 weeks with a hamstring injury he sustained against Fenerbahce in the Champions League play-off before it was later announced that France defender Mathieu Flamini had re-signed for the Gunners.
"We are very pleased Mathieu has agreed to rejoin us,'' Wenger said on www.arsenal.com.
"He is a player of real quality, with a fantastic work rate and great mentality."
Manchester City defender Joleon Lescott believes his side need to rediscover the "desire to win" that guided them to victory over Newcastle as they look to bounce back from their 3-2 defeat at newcomers Cardiff when they host Hull in the first match of the weekend.
He told the club's official website: "Even when it was the second half against Newcastle and we scored the third goal and could see the game was over for new with them being down to 10 men, we still had the desire to score and press them high and apply ourselves in the right way which the manager has pressed into us right from the pre-season.
"No matter what the situation of the game he wants us to have an identity and play the same way."
In Saturday's other games, Cardiff host Everton, Newcastle face Fulham, Norwich meet Southampton, Stoke visit West Ham and Crystal Palace look for their first point of the season at home to Sunderland.
The remaining match of the weekend sees West Brom host Swansea.
Saturday's Barclays Premier League Fixtures
Manchester City vs Hull
West Ham vs Stoke
Cardiff vs Everton
Norwich vs Southampton
Newcastle vs Fulham
Crystal Palace vs Sunderland
Sunday's Barclays Premier League Fixtures
West Brom vs Swansea
Liverpool vs Man United
Arsenal vs Tottenham