Northern Irishman believe it is too early to think about winning the Premier League.
Liverpool will remain top of the Premier League with a win over Southampton at the weekend but manager Brendan Rodgers feels it is still far too soon to discuss a potential title challenge.
The Reds have 10 points from their first four Premier League matches, with 1-0 wins over Stoke, Aston Villa and Manchester United and a 2-2 draw at Swansea.
After Southampton’s visit to Anfield, Liverpool face a run of games against Sunderland, Crystal Palace, Newcastle and West Bromwich Albion before travelling to Arsenal on November 2.
They also have Luis Suarez set to return from a 10-match suspension for biting Chelsea’s Branislav Ivanovic when they head to Manchester United in the League Cup on Wednesday.
Rodgers feels it will only be possible to judge his team’s prospects for the season once they’ve played their 10th game of the campaign at Arsenal.
Asked about Liverpool’s chances of a push for a first title since 1990, Rodgers said: “I haven’t even considered that at all. Our expectation is to improve as a team.
“We’ll assess it after 10 games and then at the halfway point and we’ll have a more realistic idea of where we can be.
“There’s a lot more to come. We’ve made a good start and people will say that it’s early stages, as will I, but these are still hurdles you have to get over.
“We’re on 10 points already and at the end of last season we finished on 61 points and we talked about those extra 10 points that might have taken us into the Champions League.
“At this early stage we’ve got them. I believe the team has still got a lot of improving, only because of the nature of what I’ve seen in the games and the potential we have in the players still to grow.”
The Northern Irishman added: “We get Luis back next week which is a world-class signing coming into the picture again.”
Suarez serves the final game of his ban against Southampton, while Daniel Agger should be available to face the Saints following a rib injury.
Philippe Coutinho is facing six weeks on the sidelines after undergoing shoulder surgery and defenders Glen Johnson and Aly Cissokho are also out of action.
Southampton were the last side to beat the league leaders, winning 3-1 at St Mary’s in March thanks to goals from Morgan Schneiderlin, Rickie Lambert and Jay Rodriguez.
Since that day Liverpool have gone 12 Premier League matches without defeat but Saints have struggled, winning only one of their last 10 league games, scoring just five times and not finding the net from open play at all this season.
Lambert will be looking to improve those statistics, especially as the England forward was on Liverpool’s books as a youngster before having to begin his career in the lower leagues.
The 31-year-old has two goals from three appearances for his country but just one for his club this term, a penalty against West Brom on the opening day.
Lambert drew a frustrating blank on Sunday during Southampton’s goalless draw with West Ham but coach Mauricio Pochettino is confident the forward will soon recapture the form that saw him score 15 times last season.
“He is very much 100 percent focused,” the former Argentina defender said. “He’s focused on scoring goals. After the game against West Ham he was angry, as any striker would be, because he didn’t score a goal to get the win for the team.”