The Egypt international is within striking distance of Rush’s record of 47 goals in a season for the Merseyside club.
Salah bolstered his chances of surpassing Rush’s tally with a four-goal haul in Liverpool FC’s 5-0 win over Watford in the Premier League before the international break.
The Reds will take on relegation candidates Crystal Palace in their next Premier League at Selhurst Park in Saturday’s early kick-off.
Liverpool FC will switch their attention to the first leg of their Champions League quarter-final with Premier League leaders Manchester City next week.
Salah has at least nine games left to score 12 goals and beat Rush’s record to cap what has been an incredible debut season at the Anfield outfit.
Former Liverpool FC striker Rush admitted that he would be delighted to see humble Salah surpass his 47 goals.
“You can look at Fernando Torres and Luis Suarez and he (Salah) is up there with any Liverpool forward to have come in [during the Premier League era],” Rush told Sky Sports News.
“He’s been absolutely amazing but the thing with Salah is that he is so down-to-earth as well.
“The game against Watford was the best I have ever seen him play, he was untouchable – not just because of his four goals but also because he wasn’t selfish and was trying to make goals for his team-mates.
“There are only two players I have seen that can play at that level, and that’s Lionel Messi and Cristiano Ronaldo.”
Salah moved to Liverpool FC in a £39m deal from Serie A giants AS Roma in the 2017 summer transfer window.
The Reds haven’t won the Premier League title but finished in second place in 2002, 2009 and 2014.
Liverpool FC are two points behind second-placed Manchester United.
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