Jurgen Klopp's side have beaten both Chelsea and Manchester City away from home since the German took over as manager, and put six goals past Southampton to book their place in the League Cup semi-finals on Wednesday.
The Merseyside outfit's form has seen them rise to sixth in the table and to within six points of leaders Manchester City.
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And Gerrard - who has been training with the first-team squad following the culmination of his first MLS season with LA Galaxy - believes a continuation of their recent displays will see Liverpool challenge for the title this term.
"At the moment they're performing the best in the league," he told RTE Radio One. "If they can keep that up, they'll be involved in the title race.
"With the new manager we don't want to have unrealistic expectations. We just need to take it one game at a time and hopefully success will come."
Liverpool have won seven of their last eight games in all competitions, though Klopp has frequently played down his side's chances of a title challenge.