The Reds have failed to find any sort of consistency this season since Klopp took over from Brendan Rodgers in October, and are sitting ninth in the Premier League table with just nine matches to go.
However, they were unfortunate to lose the Capital One Cup final on penalties to Manchester City, and are still competing on the European front, with a Europa League quarter-final tie against Klopp's old club Borussia Dortmund on the horizon.
Rush, who is Liverpool's record goalscorer with 351 goals across two spells with the club, insists that there is no reason why the Reds cannot still qualify for the Champions League at the end of the current campaign.
The former Wales striker claimed, as quoted by the Belfast Telegraph: "This season is not over yet for Liverpool. I still think the top four must be the aim - and I think it is achievable. I said it at the start of the season and I still believe that now.
"We are still in the Europa League, it is a difficult draw but I think the winners of that tie could go on and win it. So there is still a lot to play for this season."
Rush's claim may seem an ambitious one at face value, with Liverpool down in ninth in the league table, but a closer look suggests it is far from mission impossible.
Although the Reds are currently seven points off a Champions League place, they have at least one game in hand over most of their rivals for a European spot and have more than an outside chance of making up the ground on the top four.
However, Rush's suggestion that next season may be when Liverpool fans can expect a significant improvement is perhaps a more realistic one, with Klopp looking ahead to his first summer transfer window and pre-season as manager.