Salah's goal against Bournemouth in Saturday's English Premier League game took his tally for the ongoing campaign to 40, making him only the third Kops to accomplish the feat, after Rush, who did it twice, and Roger Hunt.
However, the 25-year-old is eight goals away from eclipsing Rush's haul of 47 efforts, set in the 1983-84 season to help the Kops clinch a treble.
And the Egypt international who has four Premier League games, a two-legged Champions League semi-final clashes, and a final should Jurgen Klopp's side steer past AS Roma in the last four, to claim to the 'No. 1' spot said he would be 'very happy' to accomplish the feat.
"There's a big chance to break the record, to be No. 1 for a club like Liverpool, it's something huge,'' Salah told Premier League Productions.
"I will be very happy if I break it. I'm happy about 40, I want to keep scoring, I want to be No. 1 for the record.
"It's always good when you see your name with legends of a club like Liverpool, it's a different feeling and I'm very happy about that.
"But I always try to look at myself and I want more. I have 40 now, I'm telling myself, 'Why not? You can be No. 1!'
"I will try my best to break the record but, as I've said before, we play as 11 players, I play for the team.
"It's not about individual awards, it's something for the team. I'm sure if I have a chance to give it to someone else to score, I will -- it's not about me, it's about us.''
Salah continues his hunt for ultimate glory in his 46th appearance for Liverpool as the Merseyside outfit try West Bromwich Albion for size in Saturday's top-flight tie.