The Reds haven't claimed silverware since their League Cup triumph in 2012, and are yet to win a trophy under Brendan Rodgers as they narrowly missed out on the top-flight crown last season.
Gerrard is adamant that his side have the quality to challenge for silverware in at least one of the four competitions they are entering this season.
"Without getting too carried away I think we are now a very good team and I think we can become excellent as there is still room for improvement," he told NBC.
"The rule at Liverpool is quite clear. You try to win every competition you enter. [Rodgers] has been here for two years and I think he is desperate to get a trophy in the cabinet - that is goal number one.
"It is very important we maintain our place in the Champions League but after the journey we went on last year and the confidence we gained from it I think we are genuine title contenders as we have proved we can mix it with anyone in this league."