Salah has already established himself as a Liverpool legend - alongside former defender Carragher - after scoring 218 goals in his first 360 appearances for the Merseyside club across all competitions.
Only Ian Rush (339) and Roger Hunt (263) have scored more goals for Liverpool than Salah in the club's 132-year history.
Salah has scored 160 Premier League goals for the Reds, having netted another two while playing for Chelsea in the 2013-14 campaign.
The 32-year-old moved up to ninth on the all-time list of the Premier League's leading scorers on Sunday when he netted the opening goal in Liverpool's 2-1 win over his former club at Anfield.
He is now just two goals away from overtaking Jermain Defoe in eighth place, while he is 13 behind Arsenal icon Thierry Henry in seventh, 15 shy of Frank Lampard in sixth and 98 below record-holder Alan Shearer.
Salah's current contract is due to expire in June, but Carragher believes he will be motivated to sign a new deal by the prospect of overtaking more icons on the Premier League's list of top marksmen.
Carragher was part of the Sky Sports punditry team for Liverpool's victory over Chelsea on Sunday and he said after full-time: 'Salah will have an eye on Henry and Lampard.
'Stats like this are one of the reasons I think Salah will sign a new contract at Liverpool. I'm not saying he's selfish.'
Jamie Carragher, pictured in the Sky Sports studio at Anfield, thinks Salah will stay at Liverpool
Former Liverpool and Chelsea striker Daniel Sturridge then said: 'Anyone who's an attacker, who wants to be known as the best, you have to be obsessed with things like that.
'Top three for sure in Liverpool's history. I think he wants to add to that legacy. When I met him at Liverpool I don't think he thought he would be where he is today. How he performs, it's like he's untouchable.'
Carragher - who played in 737 games for Liverpool between 1996 and 2013 - added: 'He's not an out and out striker. For a wide striker, unbelievable.'