The Egyptian's dramatic 84th-minute winner during Saturday's 2-1 comeback victory at Crystal Palace took his tally to 29 top-flight strikes and 37 overall this term.
Salah's impressive Premier League haul equals the benchmark set by former Chelsea striker Didier Drogba, who netted the same amount during 2009-10.
However, the Reds' No.11 has reached 29 in one game fewer than Drogba - and, with six Premier League matches still to play this season, he could yet surpass the ex-Ivory Coast star.
Salah is also on course to scoop this season's Golden Boot award as the Premier League's top scorer.
His composed finish at Selhurst Park moved him five goals clear of Tottenham Hotspur's Harry Kane and eight ahead of Manchester City striker Sergio Aguero.
The all-time record for the most goals scored in a 38-game Premier League season stands at 31 and is jointly held by Luis Suarez (2013-14), Cristiano Ronaldo (2007-08) and Alan Shearer (1995-96).