Jurgen Klopp's side suffered their third loss in succession when they were knocked out of the FA Cup by Wolverhampton Wanderers on Saturday, continuing a downward spiral that began at the beginning of January.
The Reds have won just one of their eight games since the turn of the year - an FA Cup third-round replay victory over Plymouth Argyle - and have failed to win in their last four Premier League games.
Having looked like realistic contenders for league honours earlier in the season, Liverpool have fallen to fourth and find themselves 10 points behind Chelsea, who they welcome to Anfield on January 31.
"The last three games have been very disappointing because of the teams we lost against," Rush told RTE.
"But [we have] a big chance now against Chelsea to try and get back to normal.
"Sometimes people get a bit too excited. At the start of the season I said if Liverpool can finish in the top four and win a trophy it'd be a fantastic season.
"What you're looking at now, the main aim is to still finish in that top four."
Rush enjoyed a trophy-laden career with Liverpool during two stints at Anfield, winning five First Division titles, two European Cups and lifting the FA Cup three times.
While acknowledging that Chelsea are in a solid position at the summit of the league, the former striker believes that a Liverpool win could have the effect of shaking up the race.
"Chelsea look like really strong favourites to win the league to tell you the truth and our job is to stay in the top four," added the 55-year-old.
"Saying that, if we go and beat Chelsea, it opens up a little bit and that's when it starts again."