Jurgen Klopp's side have taken four points from their opening two matches and booked their place in the group stages of the Champions League with an emphatic 4-2 win over Bundesliga side Hoffenheim at Anfield in midweek.
Manchester United have a 100 per cent record after their first three matches and sit two points clear of neighbours Manchester City at the summit, but Brazil international Firmino believes it is hard to identify an outright favourite to be crowned champions - something that could play into Liverpool's hands.
"We must at least repeat our performance of last year by finishing in the top four - and then fight for the title," Firmino told the Mirror.
"The team is also very motivated by the experience of being back in the Champions League. The target is to finish in the best possible position and we are aiming high.
"I think we have a chance because the Premier League is a very open competition this year. For me there doesn't exist an out-and-out favourite.
"That's what makes the season exciting. All the squads have improved but there isn't one single 'super team'. Everybody will believe they have a chance."
Remember the last time we faced Arsenal early on in a season?— Liverpool FC (@LFC) August 26, 2017
Liverpool were made to work for an edgy 1-0 win over Crystal Palace at Anfield last weekend and Firmino acknowledges the Reds can afford few slips on home soil if they are to mount a credible challenge.
"The key for us is to win our games at Anfield and make it an impossible place for rivals to visit," the Brazil international added.
"But you can see it will be a closer title race than in the past. So we need to take our opportunity."
Liverpool will once again be without Firmino's compatriot Philippe Coutinho against Arsenal, with the Barcelona target officially laid low by illness, while reports early on Sunday suggested Klopp would select Loris Karius in goal and omit regular number one Simon Mignolet from the matchday 18.