Salah, 25, scored four goals in the 5-0 thrashing over Watford on Saturday evening to take his tally to 28 goals and 10 assists in 30 Premier League games.
His 36 goals in all competitions also broke the long-standing record of Fernando Torres of 33 - for the best debut campaign with the Reds.
The Egypt international now leads Messi by four goals in the race for the top scorer in Europe and his manager Jurgen Klopp concedes he's close to reaching the elite level of the five-time Ballon d'Or winner.
"I don't think Mo or anybody else wants to be compared with Lionel Messi – he is the one who has been doing what he's been doing for what feels like 20 years or so," he said after the game, as quoted by the Echo. "The last player I know who had the same influence on a team performance was Diego Maradona.
"But Mo is in a fantastic way, that's for sure. As it always is in life, if you have to have the skills you have to show that constantly and consistently, and he is very good. He helps us a lot."
Mohamed Salah (Liverpool): 56 points (28 goals)
Lionel Messi (Barcelona): 48 points (24 goals)
Harry Kane (Tottenham): 48 points (24 goals)
Edinson Cavani (PSG): 48 points (24 goals)
Ciro Immobile (Lazio): 48 points (24 goals)