He went out on loan again, to AS Roma, who eventually signed him in 2016, before Liverpool broke their transfer record to bring him to Merseyside before the current campaign got underway.
Salah has been a revelation since returning to England, and is the league's top scorer so far with nine goals in 12 appearances.
Klopp put Salah's struggles at Chelsea down to inexperience, saying he was not surprised the Egypt international failed to force his way into a side full of seasoned players who won the title the season after he was first loaned out.
"He was very young, in a very strong team and he didn't come through. That happens very often," Klopp told a news conference.
"Another player in a similar situation is Kevin de Bruyne... doing not too bad for (Manchester) City now. It was difficult in these times to come into the team. They had a fantastic offensive line and were successful."
Belgian De Bruyne is currently in the form of his life, with his range of passing and eye for goal making him a formidable threat for the league leaders.
Like Salah, he left Chelsea while current Manchester United boss Jose Mourinho was in charge of the London club, and Klopp described Salah's decision to make his name elsewhere as "completely normal".
"Nobody is to blame for that and for sure not Mo," Klopp added. "He took his next chance, went on loan to Fiorentina and made the transfer to Rome and then came to Liverpool.
"He improved a lot for sure, especially physically and he was always a good player. I don't think he has to prove anything because it is a completely normal situation.
"If he would have played better at Chelsea we would not have him probably so I'm happy about the situation."
Midfielder Emre Can is a doubt for the Chelsea match on Saturday, but first-choice central defender Joel Matip is back in full training after missing Liverpool's last two games with a thigh strain.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
