The Mirror says Klopp demanded the Egyptian get back and defend, and was unhappy with Salah jogging around the field.
After a discussion with his assistant Pep Lijnders, Klopp opted to replace Salah with Alex Oxlade-Chamberlain - a decision that went down badly, and not just with the forward.
The Liverpool forward's agent was among those to react to the substitution, tweeting a full stop.
Former Reds star Jermaine Pennant, meanwhile, told Stadium Astro: "I'm concerned that you're bringing him off. You don't bring off a player of that stature.
"Not because he's bigger than the club, but because what he can do on the pitch.
"He can produce magic, we've seen that every season that he's played for Liverpool.
"He can be quiet for 80 minutes and bring out one piece of magic when they need it. In a game like this, you should always have Salah on the pitch.
"Bringing on Jota, great substitution. If they would have had Firmino, Jota, Mane and Salah on the pitch, they would have put Chelsea on the back foot even more.
"Taking him off, I was baffled. You should always keep Salah on the pitch. You can't bite your nose to spite your face."