Salah, who joined the Reds last summer in a £37million move from Roma, scored his 30th Premier League goal of the season against Bournemouth last weekend.
The strike, which sealed a comfortable 3-0 win for third-placed Liverpool, ensured Salah became the African player to have scored the most Premier League goals in a single season.
Ivorian legend Drogba previously held the record, after bagging 29 goals in the 2009-10 season for Chelsea.
In a message to Salah on Instagram, Drogba said: It was just a matter of days before this guy put my goal record as number one African Premier League top scorer to bed.
So proud of you lil bro to put our continent as high as you can!!! Much love and blessings, like I said before, the best is yet to come.
Salah can add another achievement to his collection by winning the Golden Boot award for being the most prolific goalscorer in Englands top-flight.
The Egypt international, who was sold by Chelsea in 2016, currently leads Tottenham and England striker Harry Kane by four goals.
Speaking after Liverpools 3-0 win over Bournemouth, manager Jurgen Klopp said of Salah: Its completely normal that a boy in that situation wants to be top of the scoring list, the Golden Boot.
We will not be in his way. But we cannot force it; so, pass, shoot, pass, shoot, thats the normal thing to do.
Its good and impressive – what a number, wow! And what a number we scored as a team in the whole season, thats crazy.
Thats really good but we have to carry on, there are a few games to come.