The Sky Blues cantered to the title last season, finishing 19 points clear of second-placed Manchester United.
After spending £161million in the summer, Firmino thinks his Liverpool team now have it all takes to topple the reigning champions.
"We have the team and squad to fight for the titles of both competitions," Firmino told Goal.
"Last season it was like that, when we reached the Champions League final and also did very well in the Premier League, although City managed to open a good lead and did not give anyone a chance to catch up.
"But the club knew how where strengthen and brought important players, including them Alisson, Fabinho and [Xherdan] Shaqiri. We have everything we need to have another great season."