The Anfield outfit have struggled to establish themselves among the top four in the Premier League in recent seasons and their League Cup success in 2012 remains their only major trophy in the past seven years.
But the England international, who signed a new two-year deal this month, feels that the club are not far away from collecting honours.
"Is success around the corner? I hope so," the 33-year-old told The Australian.
"We have bought well in the off-season and if we can get another two players in key areas then we have a good chance."
Gerrard also reserved praise for manager Brendan Rodgers, who led the club to a seventh-place finish last term.
"We have a great relationship," he continued. "Brendan has shown a lot of faith in me both on and off the field. It is early days, but I am sure our relationship will continue to grow.
"We are moving in the right direction. We are playing nice football and hopefully the owners continue to back him and he is able to add to the squad to make it stronger so we can compete for trophies."
Rodgers has been busy in the transfer market ahead of the new campaign, bringing in Kolo Toure, Luis Alberto, Iago Aspas, Simon Mignolet and Danny Wilson.
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