Salah has now scored 314 goals in a brilliant career for club and country, with stats app Five Star Football saying he equalled former Egypt captain Hossam Hassan's record with a penalty in Liverpool's 1-0 win over Fulham on Wednesday.
The goal was also his 186th strike for Liverpool since joining in 2017, moving level with former captain Steven Gerrard, the fifth-highest scorer in the club's history. Ian Rush leads the Liverpool all-time list with 346.
Salah has now also reached 30 goals this season and a century of goals at Liverpool's iconic stadium Anfield.
"I think as an offensive player, you need to have this desire to score goals, but a lot of people forget how many goals he sets up, so he's just always, very, very often involved in the goals," Klopp told Sky Sports after Liverpool's 1-0 Premier League win.
"A lot of other players don't appreciate people enough when they are still playing, and for us, it's clear he's an all-time great," he added.
Egypt's 30-year-old skipper Salah is Liverpool's record Premier League scorer with 136 goals and has won the Champions League, Premier League, FA Cup and League Cup with the club.
On the international front there is some debate about the precise number of goals for both players. Salah has 51, but two of those came in a semi-official 10-0 friendly win against Swaziland in 2013.
Hossam, who won 176 caps during his stellar 19-year international career that brought three African Nations Cup titles, is credited with 76, though several of those are considered to have come in unofficial matches.
With Saturday's win. Klopp's side are fifth in the table and still in with an outside chance of making it to the Champions League next season, and they need to keep winning just in case anyone above them slips up.
"It's probably a little bit more exciting than a few teams wanted for us, it's good that we could get into that region of the table again, but we have to make sure that we keep the teams behind us ... nothing is decided," he said as the season approaches its climax.
"We have three games to go and then, finally, a bit of a longer break, which is very helpful. You could see that today -- Brentford had a full week in between their games, we played three days ago," Klopp said.
"It's a massive difference, especially in the latter stages of the game, (but) the boys got through it, and I'm really happy about it."
Information from Reuters contributed to this report.